__source_repo string | question string | eval_solution string | solution string | eval_internal_cot string | raw_eval_prompt string | judge_correct bool | judge_reasoning string | __orig_idx int64 | __chunk_idx int64 | eval_solution__chunked string | eval_prompt list | eval_steps list | steps_word_count int64 | trace_word_count int64 | word_count_diff int64 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
1643 x 2927
Think step by step. | To solve the multiplication \(1643 \times 2927\), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(1643\) by each digit of \(2927\) (from right to left), shifting the partial results appropriately.
\[
\begin{align*}
2927 &= 2000... | 4809061 | What is the solution to the long multiplication equation below?
1643 x 2927
Think step by step. | true | The provided solution correctly calculates the product of 1643 and 2927 using long multiplication and verifies the result through different methods. The final answer of 4,809,061 matches the ground truth solution. | 707 | 0 | To solve the multiplication \(1643 \times 2927\), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(1643\) by each digit of \(2927\) (from right to left), shifting the partial results appropriately.
\[
\begin{align*}
2927 &= 2000... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the multiplication \\(1643 \\times 2927\\), we can use the **long multiplication** method. Here's a step-by-step breakdown:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thought",
"subgoal": "Setup a plan to solve t... | 228 | 244 | 16 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
2154 x 5141
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **2154** and **5141**. At first glance, this seems complex, but breaking it down into simpler, more manageable parts should make it easier. I recall that long multiplication involves multiplying each digit of the second number (5141) by the fir... | 11073714 | What is the solution to the long multiplication equation below?
2154 x 5141
Think step by step. | true | The provided solution and the calculations have been carried out methodically with detailed breakdowns leading to the correct final result of 11073714. The numerical checks through both the stepwise method and standard long multiplication confirm that the calculations are accurate. | 708 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **2154** and **5141**. At first glance, this seems complex, but breaking it down into simpler, more manageable parts should make it easier. I recall that long multiplication involves multiplying each digit of the second number (5141) by the fir... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to multiply two large numbers: **2154** and **5141**. At first glance, this seems complex, but breaking it down into simpler, more manageable parts should make it easier. I recall that long multiplication involves m... | 772 | 783 | 11 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
6078 x 4326
Think step by step. | To solve the multiplication problem \( 6078 \times 4326 \), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 6078 \) by each digit of \( 4326 \), starting from the rightmost digit, and then sum the partial results.
\[
\begin{ali... | 26293428 | What is the solution to the long multiplication equation below?
6078 x 4326
Think step by step. | true | The solution presented in the long multiplication method is correct, and the final answer matches the ground truth solution (26293428). The formatting of the final answer with commas does not affect its correctness in value. | 709 | 0 | To solve the multiplication problem \( 6078 \times 4326 \), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 6078 \) by each digit of \( 4326 \), starting from the rightmost digit, and then sum the partial results.
\[
\begin{ali... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the multiplication problem \\( 6078 \\times 4326 \\), we'll use the **long multiplication** method. Here's a step-by-step breakdown:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thought",
"subgoal": "Setup a plan t... | 203 | 218 | 15 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
4195 x 2914
Think step by step. | To solve the long multiplication equation \( 4195 \times 2914 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 4195 \) by each digit of \( 2914 \), accounting for place values, and then sum the results.
### Step 1: Break down the mul... | 12224230 | What is the solution to the long multiplication equation below?
4195 x 2914
Think step by step. | true | The solution provided accurately computes the product of 4195 and 2914 using the distributive property, and the final result matches the ground truth solution of 12222430. | 710 | 0 | To solve the long multiplication equation \( 4195 \times 2914 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 4195 \) by each digit of \( 2914 \), accounting for place values, and then sum the results.
### Step 1: Break down the mul... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 4195 \\times 2914 \\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \\( 4195 \\) by each digit of \\( 2914 \\), accounting for place ... | 365 | 365 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
2116 x 4698
Think step by step. | To solve the long multiplication equation \(2116 \times 4698\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, accounting for their place values, and then summing all the partial ... | 9940968 | What is the solution to the long multiplication equation below?
2116 x 4698
Think step by step. | true | The given solution accurately breaks down the multiplication of 2116 by 4698 using the distributive property, calculates each part correctly, and sums the partial products to arrive at the correct final answer of 9940968, which matches the ground truth solution. | 711 | 0 | To solve the long multiplication equation \(2116 \times 4698\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, accounting for their place values, and then summing all the partial ... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\(2116 \\times 4698\\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, account... | 191 | 205 | 14 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
9760 x 6114
Think step by step. | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a straightforward multiplication of two large numbers: 9760 and 6114. My goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I recall th... | 59672640 | What is the solution to the long multiplication equation below?
9760 x 6114
Think step by step. | true | The solution correctly arrived at the final product of the multiplication of 9760 and 6114, which is 59,672,640. The solution process involved breaking down the multiplication into manageable parts, verifying the result through both the distributive property and standard long multiplication, which led to consistent res... | 712 | 0 | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a straightforward multiplication of two large numbers: 9760 and 6114. My goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I recall th... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to understand what the problem is asking. It's a straightforward multiplication of two large numbers: 9760 and 6114. My goal is to find the product of these two numbers.",
"equation": "",
"finished": true,
... | 779 | 779 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
4572 x 7344
Think step by step. | To solve the multiplication problem \( 4572 \times 7344 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication using the distributive property
We can express \( 7344 \) as \( 7000 + 300 + 40 + 4 \). Multiplying \( 4572 \) by each of these component... | 33576768 | What is the solution to the long multiplication equation below?
4572 x 7344
Think step by step. | true | The solution provided used the long multiplication method accurately, performed the calculations correctly, and arrived at the final answer, which matches the ground truth solution when formatted without commas. | 713 | 0 | To solve the multiplication problem \( 4572 \times 7344 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication using the distributive property
We can express \( 7344 \) as \( 7000 + 300 + 40 + 4 \). Multiplying \( 4572 \) by each of these component... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the multiplication problem \\( 4572 \\times 7344 \\), we can use the **long multiplication** method. Here's a step-by-step breakdown:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thought",
"subgoal": "Setup a plan ... | 244 | 231 | -13 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
4586 x 1019
Think step by step. | To solve the multiplication \( 4586 \times 1019 \), we can break it down using the **distributive property of multiplication over addition**. Here's a step-by-step solution:
### Step 1: Break down the multiplier (1019)
Notice that \( 1019 \) can be written as \( 1000 + 20 - 1 \). This allows us to multiply \( 4586 \) ... | 4673134 | What is the solution to the long multiplication equation below?
4586 x 1019
Think step by step. | true | The solution follows a correct approach using the distributive property, and all calculations are verified accurately with both parts leading to the same final result. The final answer in the solution matches the ground truth solution exactly. | 714 | 0 | To solve the multiplication \( 4586 \times 1019 \), we can break it down using the **distributive property of multiplication over addition**. Here's a step-by-step solution:
### Step 1: Break down the multiplier (1019)
Notice that \( 1019 \) can be written as \( 1000 + 20 - 1 \). This allows us to multiply \( 4586 \) ... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the multiplication \\( 4586 \\times 1019 \\), we can break it down using the **distributive property of multiplication over addition**. Here's a step-by-step solution:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thoug... | 249 | 263 | 14 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
8153 x 9057
Think step by step. | To solve the long multiplication equation \( 8153 \times 9057 \), we'll break it down using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (8153) by each digit of the multiplier (9057) and then summing the partial results.
### Step 1: Break down the mul... | 73841721 | What is the solution to the long multiplication equation below?
8153 x 9057
Think step by step. | true | The solution correctly follows the steps of long multiplication using the distributive property. It accurately computes each partial product and correctly sums them to arrive at the final answer, 73841721, which matches the ground truth solution. | 715 | 0 | To solve the long multiplication equation \( 8153 \times 9057 \), we'll break it down using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (8153) by each digit of the multiplier (9057) and then summing the partial results.
### Step 1: Break down the mul... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 8153 \\times 9057 \\), we'll break it down using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (8153) by each digit of the multiplier (9057) and then... | 251 | 266 | 15 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
6746 x 9839
Think step by step. | To solve the long multiplication equation \( 6746 \times 9839 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 6746 \) by each digit of \( 9839 \), starting from the rightmost digit, and then sum the results, taking care to shift each... | 66373894 | What is the solution to the long multiplication equation below?
6746 x 9839
Think step by step. | true | The calculation and method used to arrive at the result is correct. The partial products were calculated accurately and summed appropriately. The final answer matches the ground truth solution, which confirms its correctness. | 716 | 0 | To solve the long multiplication equation \( 6746 \times 9839 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 6746 \) by each digit of \( 9839 \), starting from the rightmost digit, and then sum the results, taking care to shift each... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 6746 \\times 9839 \\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \\( 6746 \\) by each digit of \\( 9839 \\), starting from the rig... | 432 | 443 | 11 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
1650 x 4652
Think step by step. | To solve the long multiplication equation \(1650 \times 4652\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying each digit of the second number (4652) by the first number (1650) and then summing the results.
### Step 1: Break down t... | 7675800 | What is the solution to the long multiplication equation below?
1650 x 4652
Think step by step. | true | The solution correctly breaks down the multiplication of 1650 and 4652 using the distributive property and adds the results accurately. The final answer matches the ground truth solution of 7675800. | 717 | 0 | To solve the long multiplication equation \(1650 \times 4652\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying each digit of the second number (4652) by the first number (1650) and then summing the results.
### Step 1: Break down t... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation 1650 x 4652, we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying each digit of the second number (4652) by the first number (1650) and th... | 230 | 261 | 31 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
8303 x 6004
Think step by step. | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication of two large numbers: **8303** and **6004**. At first glance, multiplying these two numbers directly seems complex, but perhaps breaking it down into simpler parts can make it manageable.
### Breaking Down the ... | 49851212 | What is the solution to the long multiplication equation below?
8303 x 6004
Think step by step. | true | The solution calculated by breaking down the multiplication step-by-step using the Distributive Property, long multiplication, and verifying through different methods consistently arrives at the same result. The final answer matches the ground truth, confirming its correctness. | 718 | 0 | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication of two large numbers: **8303** and **6004**. At first glance, multiplying these two numbers directly seems complex, but perhaps breaking it down into simpler parts can make it manageable.
### Breaking Down the ... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to understand what the problem is asking. It's a multiplication of two large numbers: **8303** and **6004**. At first glance, multiplying these two numbers directly seems complex, but perhaps breaking it down into s... | 1,038 | 1,056 | 18 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
8696 x 8767
Think step by step. | To solve the multiplication problem \( 8696 \times 8767 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 8696 \) by each digit of \( 8767 \), starting from the rightmost digit, and then sum the partial results.
\[
\begin{al... | 76237832 | What is the solution to the long multiplication equation below?
8696 x 8767
Think step by step. | true | The solution correctly calculates the product of 8696 and 8767 using step-by-step long multiplication, and accurately adds all partial results to arrive at the final answer of 76,237,832, which matches the ground truth solution of 76237832. | 719 | 0 | To solve the multiplication problem \( 8696 \times 8767 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 8696 \) by each digit of \( 8767 \), starting from the rightmost digit, and then sum the partial results.
\[
\begin{al... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the multiplication problem \\( 8696 \\times 8767 \\), we can use the **long multiplication** method. Here's a step-by-step breakdown:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thought",
"subgoal": "Break down th... | 449 | 465 | 16 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
1406 x 3519
Think step by step. | To solve the long multiplication equation \(1406 \times 3519\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, appropriately shifted, and then adding all the partial results toget... | 4947714 | What is the solution to the long multiplication equation below?
1406 x 3519
Think step by step. | true | The solution provided matches the ground truth solution after confirming the calculations and the final answer, which is written in a boxed format. The arithmetic operations and methodology are also correct. | 720 | 0 | To solve the long multiplication equation \(1406 \times 3519\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, appropriately shifted, and then adding all the partial results toget... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\(1406 \\times 3519\\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, appropr... | 254 | 270 | 16 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
8145 x 7127
Think step by step. | To solve the long multiplication equation \(8145 \times 7127\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(8145\) by each digit of \(7127\) (starting from the rightmost digit) and then sum the results, taking into account the place v... | 58049415 | What is the solution to the long multiplication equation below?
8145 x 7127
Think step by step. | true | The solution accurately breaks down the multiplication using the distributive property, correctly calculates each partial product, and accurately sums these results to arrive at the final value of 58049415. The final answer matches the ground truth solution. | 721 | 0 | To solve the long multiplication equation \(8145 \times 7127\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(8145\) by each digit of \(7127\) (starting from the rightmost digit) and then sum the results, taking into account the place v... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation 8145 x 7127, we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply 8145 by each digit of 7127 (starting from the rightmost digit) and then sum the... | 303 | 336 | 33 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7805 x 2392
Think step by step. | To solve the long multiplication equation \( 7805 \times 2392 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, appropriately shifted, and then adding all the partial results tog... | 18669560 | What is the solution to the long multiplication equation below?
7805 x 2392
Think step by step. | true | The calculated product of 7805 and 2392 is 18669560, which matches the ground truth solution. The solution provided has correctly applied the distributive property and verified the results using standard long multiplication, confirming the final answer is accurate. | 722 | 0 | To solve the long multiplication equation \( 7805 \times 2392 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, appropriately shifted, and then adding all the partial results tog... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 7805 \\times 2392 \\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, appro... | 353 | 357 | 4 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
3969 x 4372
Think step by step. | To solve the long multiplication equation \( 3969 \times 4372 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, accounting for place values, and then summing all the partial prod... | 17352468 | What is the solution to the long multiplication equation below?
3969 x 4372
Think step by step. | true | The solution presented uses the distributive property to break down the multiplication of 3969 by 4372 correctly into partial products. Each component is calculated accurately according to place value, and the final summation of the partial products gives the same result as the ground truth solution when considering th... | 723 | 0 | To solve the long multiplication equation \( 3969 \times 4372 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, accounting for place values, and then summing all the partial prod... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 3969 \\times 4372 \\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, accou... | 244 | 300 | 56 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
1299 x 1957
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **1299** and **1957**. At first glance, this seems complex, but breaking it down into simpler, more manageable parts can make it easier. I recall that long multiplication involves multiplying each digit of the second number (the multiplier) by ... | 2542143 | What is the solution to the long multiplication equation below?
1299 x 1957
Think step by step. | true | The solution accurately details the step-by-step process for multiplying 1299 and 1957 using both the breakdown of the multiplier and direct long multiplication. It performs each multiplication correctly, verifies intermediate results, sums all partial products accurately, and arrives at the same final answer as the gr... | 724 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **1299** and **1957**. At first glance, this seems complex, but breaking it down into simpler, more manageable parts can make it easier. I recall that long multiplication involves multiplying each digit of the second number (the multiplier) by ... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to multiply two large numbers: **1299** and **1957**. At first glance, this seems complex, but breaking it down into simpler, more manageable parts can make it easier. I recall that long multiplication involves mult... | 954 | 965 | 11 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
2014 x 6769
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: 2014 and 6769. At first glance, this seems complex, but breaking it down into simpler, more manageable parts can make it easier. I recall that long multiplication involves multiplying each digit of the second number by the first number and then... | 13632766 | What is the solution to the long multiplication equation below?
2014 x 6769
Think step by step. | true | The solution provided correctly follows a methodical approach to multiply two large numbers, breaking down the multiplication into manageable parts and summing correctly. The final multiplication result is calculated as 13,632,766, which matches the ground truth solution given. | 725 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: 2014 and 6769. At first glance, this seems complex, but breaking it down into simpler, more manageable parts can make it easier. I recall that long multiplication involves multiplying each digit of the second number by the first number and then... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to multiply two large numbers: 2014 and 6769. At first glance, this seems complex, but breaking it down into simpler, more manageable parts can make it easier. I recall that long multiplication involves multiplying ... | 769 | 716 | -53 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
6138 x 8074
Think step by step. | To solve the multiplication problem \(6138 \times 8074\), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(6138\) by each digit of \(8074\) (from right to left), keeping track of the place values by adding zeros as needed.
\[
\be... | 49558212 | What is the solution to the long multiplication equation below?
6138 x 8074
Think step by step. | false | The solution provided calculates the product of 6138 and 8074 using long multiplication, but the final result of 49,557,212 does not match the ground truth of 49,558,212. Therefore, the solution is incorrect. | 726 | 0 | To solve the multiplication problem \(6138 \times 8074\), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(6138\) by each digit of \(8074\) (from right to left), keeping track of the place values by adding zeros as needed.
\[
\be... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the multiplication problem \\(6138 \\times 8074\\), we'll use the **long multiplication** method. Here's a step-by-step breakdown:\n\n### Step 1: Break down the multiplication\nWe'll multiply \\(6138\\) by each digit of \\(8074\\) (from right to left), ... | 259 | 273 | 14 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7615 x 2519
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **7,615** and **2,519**. Breaking this down, I recall that long multiplication involves multiplying each digit of the second number (the multiplier) by the entire first number (the multiplicand) and then adding all the partial products together... | 19182185 | What is the solution to the long multiplication equation below?
7615 x 2519
Think step by step. | true | The solution provided accurately calculates the product of 7,615 and 2,519 using both long multiplication and the grid method. It methodically verifies each step and arrives at the correct final result of 19,182,185, which matches the ground truth solution. | 727 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **7,615** and **2,519**. Breaking this down, I recall that long multiplication involves multiplying each digit of the second number (the multiplier) by the entire first number (the multiplicand) and then adding all the partial products together... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to multiply two large numbers: **7,615** and **2,519**. Breaking this down, I recall that long multiplication involves multiplying each digit of the second number (the multiplier) by the entire first number (the mul... | 678 | 688 | 10 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
5588 x 8657
Think step by step. | To solve the multiplication problem \( 5588 \times 8657 \), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 5588 \) by each digit of \( 8657 \), starting from the rightmost digit, and then sum the partial results.
\[
\begin{ali... | 48375316 | What is the solution to the long multiplication equation below?
5588 x 8657
Think step by step. | true | The solution correctly applies the long multiplication method, breaks down the multiplication into its component parts, and accurately sums the partial results. The final answer of 48,375,316 matches the ground truth solution. | 728 | 0 | To solve the multiplication problem \( 5588 \times 8657 \), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 5588 \) by each digit of \( 8657 \), starting from the rightmost digit, and then sum the partial results.
\[
\begin{ali... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the multiplication problem \\( 5588 \\times 8657 \\), we'll use the **long multiplication** method. Here's a step-by-step breakdown:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thought",
"subgoal": "Setup a plan t... | 223 | 225 | 2 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
6840 x 1868
Think step by step. | To solve the long multiplication equation \( 6840 \times 1868 \), we can break it down into simpler, more manageable steps using the **distributive property of multiplication over addition**. Here's a step-by-step solution:
### Step 1: Break down the multiplier (1868)
We can express 1868 as \( 2000 - 132 \), which sim... | 12777120 | What is the solution to the long multiplication equation below?
6840 x 1868
Think step by step. | true | The solution provided matches the ground truth solution when formatted as numerical values. The calculations leading to the final result of 12,777,120 were performed correctly, confirming that the answer is accurate. | 729 | 0 | To solve the long multiplication equation \( 6840 \times 1868 \), we can break it down into simpler, more manageable steps using the **distributive property of multiplication over addition**. Here's a step-by-step solution:
### Step 1: Break down the multiplier (1868)
We can express 1868 as \( 2000 - 132 \), which sim... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 6840 \\times 1868 \\), we can break it down into simpler, more manageable steps using the **distributive property of multiplication over addition**. Here's a step-by-step solution:",
"equation": "",
"finished... | 208 | 208 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
1135 x 7739
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **1135** and **7739**. To tackle this, I recall that long multiplication involves breaking down the problem into simpler, more manageable parts. Specifically, I can use the **distributive property** of multiplication over addition, which allows... | 8783765 | What is the solution to the long multiplication equation below?
1135 x 7739
Think step by step. | true | The provided solution correctly breaks down the multiplication process using both the distributive property and standard long multiplication, leading to the same correct result of 8,783,765. | 730 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **1135** and **7739**. To tackle this, I recall that long multiplication involves breaking down the problem into simpler, more manageable parts. Specifically, I can use the **distributive property** of multiplication over addition, which allows... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to multiply two large numbers: **1135** and **7739**. To tackle this, I recall that long multiplication involves breaking down the problem into simpler, more manageable parts. Specifically, I can use the **distribut... | 1,053 | 1,056 | 3 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7757 x 5462
Think step by step. | To solve the multiplication problem \( 7757 \times 5462 \), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 7757 \) by each digit of \( 5462 \), starting from the rightmost digit, and shift the partial results accordingly.
\[
\... | 42368734 | What is the solution to the long multiplication equation below?
7757 x 5462
Think step by step. | false | The final answer provided in the solution, 42,362,734, does not match the ground truth answer of 42,368,734. Upon reviewing the breakdown of the multiplication and the addition of the partial results, an addition error occurred somewhere in the calculation of the total, leading to the incorrect final result. | 731 | 0 | To solve the multiplication problem \( 7757 \times 5462 \), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 7757 \) by each digit of \( 5462 \), starting from the rightmost digit, and shift the partial results accordingly.
\[
\... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the multiplication problem \\( 7757 \\times 5462 \\), we'll use the **long multiplication** method. Here's a step-by-step breakdown:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thought",
"subgoal": "Setup a plan t... | 231 | 211 | -20 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
9319 x 7588
Think step by step. | To solve the multiplication problem \(9319 \times 7588\), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(9319\) by each digit of \(7588\), starting from the rightmost digit, and then sum the results.
Note: \(7588\) can be writ... | 70712572 | What is the solution to the long multiplication equation below?
9319 x 7588
Think step by step. | true | The solution correctly applies the long multiplication method step-by-step to compute the product of 9319 and 7588. The final sum of the partial results matches the ground truth solution, confirming the correctness of the final answer. | 732 | 0 | To solve the multiplication problem \(9319 \times 7588\), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(9319\) by each digit of \(7588\), starting from the rightmost digit, and then sum the results.
Note: \(7588\) can be writ... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the multiplication problem \\(9319 \\times 7588\\), we'll use the **long multiplication** method. Here's a step-by-step breakdown:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thought",
"subgoal": "Break down the m... | 211 | 223 | 12 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
8903 x 4774
Think step by step. | To solve the long multiplication equation \( 8903 \times 4774 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 8903 \) by each digit of \( 4774 \) (from right to left), shifting the partial results appropriately, and then add them tog... | 42502922 | What is the solution to the long multiplication equation below?
8903 x 4774
Think step by step. | true | The solution correctly utilizes the distributive property of multiplication to break down the problem and arrives at the final answer of 42,502,922, which matches the ground truth solution of 42502922. | 733 | 0 | To solve the long multiplication equation \( 8903 \times 4774 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 8903 \) by each digit of \( 4774 \) (from right to left), shifting the partial results appropriately, and then add them tog... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 8903 \\times 4774 \\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \\( 8903 \\) by each digit of \\( 4774 \\) (from right to left), ... | 308 | 323 | 15 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
9258 x 6709
Think step by step. | To solve the long multiplication equation \( 9258 \times 6709 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 9258 \) by each digit of \( 6709 \), starting from the rightmost digit, and then sum the partial results.
### Step 1: Brea... | 62111922 | What is the solution to the long multiplication equation below?
9258 x 6709
Think step by step. | true | The solution correctly breaks down the multiplication using the distributive property, performs each multiplication accurately, sums the partial products correctly, and verifies the result with long multiplication, ultimately confirming the final answer matches the ground truth solution (62111922). Thus, the answer in ... | 734 | 0 | To solve the long multiplication equation \( 9258 \times 6709 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 9258 \) by each digit of \( 6709 \), starting from the rightmost digit, and then sum the partial results.
### Step 1: Brea... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 9258 \\times 6709 \\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \\( 9258 \\) by each digit of \\( 6709 \\), starting from the rig... | 325 | 372 | 47 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
2499 x 6899
Think step by step. | To solve the long multiplication equation \( 2499 \times 6899 \), we can use the **distributive property of multiplication over addition**. This method breaks down the multiplication into simpler, more manageable parts. Here's a step-by-step solution:
### Step 1: Break down the second number (6899)
We can express \( 6... | 17240601 | What is the solution to the long multiplication equation below?
2499 x 6899
Think step by step. | true | The provided solution accurately followed the steps of long multiplication and the verification matches the ground truth. | 735 | 0 | To solve the long multiplication equation \( 2499 \times 6899 \), we can use the **distributive property of multiplication over addition**. This method breaks down the multiplication into simpler, more manageable parts. Here's a step-by-step solution:
### Step 1: Break down the second number (6899)
We can express \( 6... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 2499 \\times 6899 \\), we can use the **distributive property of multiplication over addition**. This method breaks down the multiplication into simpler, more manageable parts. Here's a step-by-step solution:",
"... | 374 | 379 | 5 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
1967 x 2263
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: 1967 and 2263. Multiplying large numbers can be complex, but breaking it down into simpler, more manageable parts can make the process easier. I recall that the standard method for long multiplication involves multiplying each digit of the seco... | 4451321 | What is the solution to the long multiplication equation below?
1967 x 2263
Think step by step. | true | The calculated product of 1967 and 2263 is accurately found to be 4,451,321, which matches the ground truth solution provided. | 736 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: 1967 and 2263. Multiplying large numbers can be complex, but breaking it down into simpler, more manageable parts can make the process easier. I recall that the standard method for long multiplication involves multiplying each digit of the seco... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to multiply two large numbers: 1967 and 2263. Multiplying large numbers can be complex, but breaking it down into simpler, more manageable parts can make the process easier. I recall that the standard method for lon... | 876 | 1,063 | 187 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
6210 x 4858
Think step by step. | To solve the long multiplication equation \( 6210 \times 4858 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying each digit of the second number (4858) by each digit of the first number (6210) and then summing the results.
### Step... | 30168180 | What is the solution to the long multiplication equation below?
6210 x 4858
Think step by step. | true | The provided solution uses the correct breakdown and calculation method for long multiplication and arrives at the same final result as the ground truth solution (30168180). The verification step confirms the calculation's accuracy. Thus, the solution is correct. | 737 | 0 | To solve the long multiplication equation \( 6210 \times 4858 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying each digit of the second number (4858) by each digit of the first number (6210) and then summing the results.
### Step... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 6210 \\times 4858 \\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying each digit of the second number (4858) by each digit of th... | 378 | 399 | 21 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
1833 x 2082
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **1833** and **2082**. At first glance, this seems complex, but breaking it down into simpler, more manageable parts can make it easier. I recall that long multiplication involves multiplying each digit of the second number (the multiplier) by ... | 3816306 | What is the solution to the long multiplication equation below?
1833 x 2082
Think step by step. | true | The solution correctly computes the product of 1833 and 2082 as 3,816,306 using detailed steps in both breakdown and long multiplication methods. The final result matches the ground truth solution. | 738 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **1833** and **2082**. At first glance, this seems complex, but breaking it down into simpler, more manageable parts can make it easier. I recall that long multiplication involves multiplying each digit of the second number (the multiplier) by ... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to multiply two large numbers: **1833** and **2082**. At first glance, this seems complex, but breaking it down into simpler, more manageable parts can make it easier. I recall that long multiplication involves mult... | 653 | 675 | 22 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
6965 x 4007
Think step by step. | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a straightforward multiplication of two large numbers: 6,965 and 4,007. My goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I recall t... | 27908755 | What is the solution to the long multiplication equation below?
6965 x 4007
Think step by step. | true | The solution correctly uses multiple methods to verify the multiplication of the two numbers, arriving at the accurate final product of 27,908,755, which matches the ground truth solution. | 739 | 0 | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a straightforward multiplication of two large numbers: 6,965 and 4,007. My goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I recall t... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to understand what the problem is asking. It's a straightforward multiplication of two large numbers: 6,965 and 4,007. My goal is to find the product of these two numbers.",
"equation": "",
"finished": true,... | 1,043 | 1,073 | 30 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
2714 x 7568
Think step by step. | To solve the long multiplication equation \( 2714 \times 7568 \), we'll break it down step by step using the **long multiplication method**. Here's how it works:
### Step 1: Break down the multiplication
We'll multiply \( 2714 \) by each digit of \( 7568 \), starting from the rightmost digit (units place), and shift t... | 20539552 | What is the solution to the long multiplication equation below?
2714 x 7568
Think step by step. | true | The solution correctly follows the long multiplication procedure and has accurately calculated the product of 2714 and 7568, confirming that the final answer matches the ground truth. | 740 | 0 | To solve the long multiplication equation \( 2714 \times 7568 \), we'll break it down step by step using the **long multiplication method**. Here's how it works:
### Step 1: Break down the multiplication
We'll multiply \( 2714 \) by each digit of \( 7568 \), starting from the rightmost digit (units place), and shift t... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 2714 \\times 7568 \\), we'll break it down step by step using the **long multiplication method**. Here's how it works:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thought",
"su... | 317 | 333 | 16 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
3277 x 2190
Think step by step. | To solve the long multiplication equation \( 3277 \times 2190 \), we can break it down into simpler steps using the distributive property of multiplication over addition. Here's a step-by-step solution:
### Step 1: Break down the multiplication
We can express \( 2190 \) as \( 2000 + 100 + 90 \). This allows us to mult... | 7176630 | What is the solution to the long multiplication equation below?
3277 x 2190
Think step by step. | true | The solution correctly breaks down the multiplication using the distributive property, executes each multiplication step accurately, and adds the partial results correctly. The final answer matches the ground truth solution. | 741 | 0 | To solve the long multiplication equation \( 3277 \times 2190 \), we can break it down into simpler steps using the distributive property of multiplication over addition. Here's a step-by-step solution:
### Step 1: Break down the multiplication
We can express \( 2190 \) as \( 2000 + 100 + 90 \). This allows us to mult... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 3277 \\times 2190 \\), we can break it down into simpler steps using the distributive property of multiplication over addition. Here's a step-by-step solution:",
"equation": "",
"finished": true,
"output"... | 445 | 448 | 3 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
9155 x 5785
Think step by step. | To solve the long multiplication equation \( 9155 \times 5785 \), we'll break it down using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (9155) by each digit of the multiplier (5785), considering their place values, and then adding all the partial prod... | 52961675 | What is the solution to the long multiplication equation below?
9155 x 5785
Think step by step. | false | The provided solution calculates the product of 9155 and 5785 as 52,961,675. However, the correct ground truth solution is 52,961,675, not matched as it is missing a leading zero. The addition of the partial products was done correctly, leading to the incorrect number formatting in the final answer. Therefore, while th... | 742 | 0 | To solve the long multiplication equation \( 9155 \times 5785 \), we'll break it down using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (9155) by each digit of the multiplier (5785), considering their place values, and then adding all the partial prod... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 9155 \\times 5785 \\), we'll break it down using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (9155) by each digit of the multiplier (5785), conside... | 371 | 329 | -42 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
6897 x 1292
Think step by step. | To solve the long multiplication equation \( 6897 \times 1292 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, shifting the partial results appropriately, and then adding them t... | 8910924 | What is the solution to the long multiplication equation below?
6897 x 1292
Think step by step. | true | The provided solution correctly follows the steps for long multiplication using the distributive property, providing accurate intermediate results and final addition, reaching the final answer of 8,910,924, which matches the ground truth solution. | 743 | 0 | To solve the long multiplication equation \( 6897 \times 1292 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, shifting the partial results appropriately, and then adding them t... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 6897 \\times 1292 \\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, shift... | 293 | 297 | 4 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
5918 x 1734
Think step by step. | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication of two large numbers: 5918 and 1734. The goal is to find the product of these two numbers. Since both numbers are four-digit, I recall that the standard method taught in school is the long multiplication method,... | 10261812 | What is the solution to the long multiplication equation below?
5918 x 1734
Think step by step. | true | The calculations were performed accurately using two methods and matched the ground truth solution. The final result of the multiplication was confirmed to be 10,261,812. | 744 | 0 | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication of two large numbers: 5918 and 1734. The goal is to find the product of these two numbers. Since both numbers are four-digit, I recall that the standard method taught in school is the long multiplication method,... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to understand what the problem is asking. It's a multiplication of two large numbers: 5918 and 1734. The goal is to find the product of these two numbers. Since both numbers are four-digit, I recall that the standar... | 1,128 | 1,132 | 4 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
6495 x 2209
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **6495** and **2209**. At first glance, this seems complex because both numbers are four-digit numbers. Breaking it down using the **long multiplication** method might make it more manageable.
### Breaking Down the Multiplication
Long multipl... | 14347455 | What is the solution to the long multiplication equation below?
6495 x 2209
Think step by step. | true | The solution provided correctly calculates the product of 6495 and 2209 using the long multiplication method and verifies the result through various strategies. It arrives accurately at the final product, which matches the ground truth solution of 14,347,455. | 745 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **6495** and **2209**. At first glance, this seems complex because both numbers are four-digit numbers. Breaking it down using the **long multiplication** method might make it more manageable.
### Breaking Down the Multiplication
Long multipl... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to multiply two large numbers: **6495** and **2209**. At first glance, this seems complex because both numbers are four-digit numbers. Breaking it down using the **long multiplication** method might make it more man... | 956 | 956 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7768 x 9513
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **7768** and **9513**. At first glance, this seems daunting because both numbers are in the thousands. However, breaking it down into smaller, more manageable parts can simplify the process.
### Breaking Down the Multiplication
One effective... | 73896984 | What is the solution to the long multiplication equation below?
7768 x 9513
Think step by step. | true | The provided solution arrived at the correct product of 7768 and 9513 through accurate calculations and methodologies, ultimately confirming the result matches the ground truth solution of 73896984. | 746 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **7768** and **9513**. At first glance, this seems daunting because both numbers are in the thousands. However, breaking it down into smaller, more manageable parts can simplify the process.
### Breaking Down the Multiplication
One effective... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to multiply two large numbers: **7768** and **9513**. At first glance, this seems daunting because both numbers are in the thousands. However, breaking it down into smaller, more manageable parts can simplify the pr... | 814 | 825 | 11 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
1392 x 3124
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **1392** and **3124**. Multiplying large numbers can be complex, but breaking it down into simpler, more manageable parts can make the process easier. I recall that long multiplication involves multiplying each digit of the second number (the m... | 4348608 | What is the solution to the long multiplication equation below?
1392 x 3124
Think step by step. | true | The provided solution accurately computes the product of 1392 and 3124 using two different methods and verifies each step. The final product calculated matches the ground truth solution. | 747 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **1392** and **3124**. Multiplying large numbers can be complex, but breaking it down into simpler, more manageable parts can make the process easier. I recall that long multiplication involves multiplying each digit of the second number (the m... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to multiply two large numbers: **1392** and **3124**. Multiplying large numbers can be complex, but breaking it down into simpler, more manageable parts can make the process easier. I recall that long multiplication... | 914 | 956 | 42 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
6177 x 7354
Think step by step. | To solve the long multiplication problem \(6177 \times 7354\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(6177\) by each digit of \(7354\), starting from the rightmost digit, and then sum the results, taking care to shift each partia... | 45425658 | What is the solution to the long multiplication equation below?
6177 x 7354
Think step by step. | true | The provided solution accurately applies the distributive property of multiplication, correctly computes each partial product, and sums them to arrive at the final result, which matches the ground truth solution. | 748 | 0 | To solve the long multiplication problem \(6177 \times 7354\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(6177\) by each digit of \(7354\), starting from the rightmost digit, and then sum the results, taking care to shift each partia... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication problem \\(6177 \\times 7354\\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \\(6177\\) by each digit of \\(7354\\), starting from the rightmost ... | 397 | 399 | 2 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
3050 x 5179
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **3050** and **5179**. At first glance, this seems daunting because both numbers are in the thousands. However, breaking it down into simpler, more manageable parts can make the process easier.
### Breaking Down the Multiplication
One effect... | 15795950 | What is the solution to the long multiplication equation below?
3050 x 5179
Think step by step. | true | The provided solution accurately follows the process of long multiplication, breaking down the multiplication into manageable parts, calculating each partial product correctly, and summing them to arrive at the final answer. The final answer of 15795950 matches the ground truth solution. | 749 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **3050** and **5179**. At first glance, this seems daunting because both numbers are in the thousands. However, breaking it down into simpler, more manageable parts can make the process easier.
### Breaking Down the Multiplication
One effect... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to multiply two large numbers: **3050** and **5179**. At first glance, this seems daunting because both numbers are in the thousands. However, breaking it down into simpler, more manageable parts can make the proces... | 707 | 715 | 8 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7141 x 9593
Think step by step. | To solve the long multiplication equation \(7141 \times 9593\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, accounting for place value, and then adding all the partial products... | 68503613 | What is the solution to the long multiplication equation below?
7141 x 9593
Think step by step. | false | The provided solution computes the result as 68,503,613 but the ground truth solution states the result should be 68503613 without the comma. Therefore, the two values are not the same; one has a comma separating the thousands while the other does not, indicating a formatting issue. The numerical values are equivalent ... | 750 | 0 | To solve the long multiplication equation \(7141 \times 9593\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, accounting for place value, and then adding all the partial products... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation 7141 x 9593, we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, accounting for plac... | 250 | 287 | 37 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
6709 x 6102
Think step by step. | To solve the long multiplication equation \( 6709 \times 6102 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, shifting appropriately, and then adding the results.
### Step 1: ... | 40938318 | What is the solution to the long multiplication equation below?
6709 x 6102
Think step by step. | true | The solution accurately applies the distributive property of multiplication and consistently arrives at the final result. Both the step-by-step breakdown and the verification using standard long multiplication confirm that the answer is indeed 40,938,318, matching the ground truth solution of 40938318 (where the comma ... | 751 | 0 | To solve the long multiplication equation \( 6709 \times 6102 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, shifting appropriately, and then adding the results.
### Step 1: ... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 6709 \\times 6102 \\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, shift... | 296 | 312 | 16 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
6769 x 1207
Think step by step. | To solve the multiplication problem \( 6769 \times 1207 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We can express \( 1207 \) as \( 1000 + 200 + 0 + 7 \). This allows us to multiply \( 6769 \) by each component separately and then add th... | 8170183 | What is the solution to the long multiplication equation below?
6769 x 1207
Think step by step. | true | The solution accurately breaks down the multiplication using the long multiplication method and correctly computes the partial products. The final answer obtained from both the breakdown and verification processes correctly matches the ground truth solution, confirming the solution's correctness. | 752 | 0 | To solve the multiplication problem \( 6769 \times 1207 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We can express \( 1207 \) as \( 1000 + 200 + 0 + 7 \). This allows us to multiply \( 6769 \) by each component separately and then add th... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the multiplication problem \\( 6769 \\times 1207 \\), we can use the **long multiplication** method. Here's a step-by-step breakdown:\n\n### Step 1: Break down the multiplication\nWe can express \\( 1207 \\) as \\( 1000 + 200 + 0 + 7 \\). This allows us... | 268 | 290 | 22 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
5976 x 1714
Think step by step. | To solve the long multiplication equation \(5976 \times 1714\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (5976) by each digit of the multiplier (1714), starting from the rightmost digit, and then summing up th... | 10242864 | What is the solution to the long multiplication equation below?
5976 x 1714
Think step by step. | true | The solution correctly follows the long multiplication method step by step and arrives at the same result of 10,242,864, which matches the ground truth solution. The mathematical operations have been clearly laid out and successfully verified. | 753 | 0 | To solve the long multiplication equation \(5976 \times 1714\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (5976) by each digit of the multiplier (1714), starting from the rightmost digit, and then summing up th... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\(5976 \\times 1714\\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (5976) by each digit of the multiplier (171... | 290 | 292 | 2 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7215 x 6982
Think step by step. | To solve the multiplication problem \( 7215 \times 6982 \), we can use the **long multiplication method**. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 7215 \) by each digit of \( 6982 \), starting from the rightmost digit (units place), and shift the partial results acc... | 50375130 | What is the solution to the long multiplication equation below?
7215 x 6982
Think step by step. | false | The solution provided calculates the multiplication of 7215 and 6982 incorrectly. The final summed result given is 50351130, which does not match the ground truth solution of 50375130. Therefore, the solution is incorrect. | 754 | 0 | To solve the multiplication problem \( 7215 \times 6982 \), we can use the **long multiplication method**. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 7215 \) by each digit of \( 6982 \), starting from the rightmost digit (units place), and shift the partial results acc... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the multiplication problem \\( 7215 \\times 6982 \\), we can use the **long multiplication method**. Here's a step-by-step breakdown:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thought",
"subgoal": "Understanding... | 539 | 561 | 22 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
2073 x 5000
Think step by step. | To solve the multiplication problem \( 2073 \times 5000 \), follow these steps:
### Step 1: Break down the multiplication
Notice that \( 5000 \) can be written as \( 5 \times 1000 \). So, the multiplication can be rewritten as:
\[
2073 \times 5000 = 2073 \times (5 \times 1000)
\]
### Step 2: Multiply \( 2073 \) by \(... | 10365000 | What is the solution to the long multiplication equation below?
2073 x 5000
Think step by step. | true | The solution correctly follows the procedure for multiplying 2073 by 5000 by breaking it down into manageable steps. The initial multiplication of 2073 by 5 yields 10,365, and then multiplying that result by 1000 correctly gives 10,365,000. The final boxed answer is also formatted correctly, matches the ground truth so... | 755 | 0 | To solve the multiplication problem \( 2073 \times 5000 \), follow these steps:
### Step 1: Break down the multiplication
Notice that \( 5000 \) can be written as \( 5 \times 1000 \). So, the multiplication can be rewritten as:
\[
2073 \times 5000 = 2073 \times (5 \times 1000)
\]
### Step 2: Multiply \( 2073 \) by \(... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the multiplication problem \\( 2073 \\times 5000 \\), follow these steps:\n\n### Step 1: Break down the multiplication\nNotice that \\( 5000 \\) can be written as \\( 5 \\times 1000 \\). So, the multiplication can be rewritten as:\n\\[ 2073 \\times 5000... | 131 | 133 | 2 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7376 x 3024
Think step by step. | To solve the multiplication problem \(7376 \times 3024\), we can break it down using the **distributive property of multiplication over addition**. Here's a step-by-step solution:
### Step 1: Break down the multiplier (3024)
The multiplier \(3024\) can be expressed as:
\[ 3024 = 3000 + 20 + 4 \]
### Step 2: Multiply ... | 22305024 | What is the solution to the long multiplication equation below?
7376 x 3024
Think step by step. | true | The solution correctly applies the distributive property to break down the multiplication of 7376 and 3024, calculates each part accurately, and sums the partial products correctly, confirming the final answer matches the ground truth solution. | 756 | 0 | To solve the multiplication problem \(7376 \times 3024\), we can break it down using the **distributive property of multiplication over addition**. Here's a step-by-step solution:
### Step 1: Break down the multiplier (3024)
The multiplier \(3024\) can be expressed as:
\[ 3024 = 3000 + 20 + 4 \]
### Step 2: Multiply ... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the multiplication problem 7376 x 3024, we can break it down using the **distributive property of multiplication over addition**. Here's a step-by-step solution:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thought",
... | 243 | 281 | 38 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
4297 x 2561
Think step by step. | To solve the long multiplication equation \(4297 \times 2561\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, appropriately shifted, and then adding all the partial results toget... | 11004617 | What is the solution to the long multiplication equation below?
4297 x 2561
Think step by step. | true | The solution accurately demonstrates the process of long multiplication using the distributive property, correctly calculates each partial product, sums them, and reproduces the final result. The final answer presented in the boxed format matches the ground truth solution, confirming completeness and correctness. | 757 | 0 | To solve the long multiplication equation \(4297 \times 2561\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, appropriately shifted, and then adding all the partial results toget... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\(4297 \\times 2561\\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, appropr... | 260 | 282 | 22 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
1399 x 9181
Think step by step. | To solve the long multiplication equation \(1399 \times 9181\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying each digit of the second number (9181) by the first number (1399) and then adding the results.
### Step 1: Break down th... | 12844219 | What is the solution to the long multiplication equation below?
1399 x 9181
Think step by step. | false | The computed final result of the multiplication is incorrect because the provided solution's answer (12,843,219) does not match the ground truth solution (12,844,219). Hence, the solution is not correct. | 758 | 0 | To solve the long multiplication equation \(1399 \times 9181\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying each digit of the second number (9181) by the first number (1399) and then adding the results.
### Step 1: Break down th... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\(1399 \\times 9181\\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying each digit of the second number (9181) by the first number (... | 230 | 230 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
4274 x 3246
Think step by step. | To solve the long multiplication equation \(4274 \times 3246\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(4274\) by each digit of \(3246\) (from right to left), shift the partial results accordingly, and then add them together.
###... | 13873404 | What is the solution to the long multiplication equation below?
4274 x 3246
Think step by step. | true | The submitted solution accurately describes the process of long multiplication using the distributive property and provides correct calculations and a final answer that matches the ground truth. | 759 | 0 | To solve the long multiplication equation \(4274 \times 3246\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(4274\) by each digit of \(3246\) (from right to left), shift the partial results accordingly, and then add them together.
###... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\(4274 \\times 3246\\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \\(4274\\) by each digit of \\(3246\\) (from right to left), shift ... | 441 | 346 | -95 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
3644 x 6720
Think step by step. | To solve the multiplication problem \( 3644 \times 6720 \), we can break it down into simpler, more manageable steps. Here's a detailed step-by-step solution:
### Step 1: Break down the multiplication
We can use the **distributive property of multiplication** to break the problem into smaller parts. Notice that \( 672... | 24487680 | What is the solution to the long multiplication equation below?
3644 x 6720
Think step by step. | true | The calculated solution matches the ground truth solution of 24487680. All steps were correctly executed, and the use of the distributive property was appropriately applied. | 760 | 0 | To solve the multiplication problem \( 3644 \times 6720 \), we can break it down into simpler, more manageable steps. Here's a detailed step-by-step solution:
### Step 1: Break down the multiplication
We can use the **distributive property of multiplication** to break the problem into smaller parts. Notice that \( 672... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the multiplication problem \\( 3644 \\times 6720 \\), we can break it down into simpler, more manageable steps. Here's a detailed step-by-step solution:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thought",
"subgo... | 353 | 333 | -20 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
3868 x 4542
Think step by step. | To solve the multiplication problem \( 3868 \times 4542 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 3868 \) by each digit of \( 4542 \), starting from the rightmost digit, and then sum the partial results.
\[
\begin{al... | 17568456 | What is the solution to the long multiplication equation below?
3868 x 4542
Think step by step. | true | The solution correctly applies long multiplication step-by-step, accurately multiplying each digit and summing the partial results to arrive at the correct final product of 3868 and 4542, which is indeed 17568456. | 761 | 0 | To solve the multiplication problem \( 3868 \times 4542 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 3868 \) by each digit of \( 4542 \), starting from the rightmost digit, and then sum the partial results.
\[
\begin{al... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the multiplication problem \\( 3868 \\times 4542 \\), we can use the **long multiplication** method. Here's a step-by-step breakdown:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thought",
"subgoal": "Setup a plan ... | 241 | 255 | 14 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
8073 x 1930
Think step by step. | To solve the long multiplication equation \( 8073 \times 1930 \), we can break it down into simpler, more manageable steps. Here's a detailed step-by-step solution:
### Step 1: Break down the multiplication
The number \( 1930 \) can be expressed as \( 2000 - 70 \). This allows us to rewrite the multiplication as:
\[
8... | 15580890 | What is the solution to the long multiplication equation below?
8073 x 1930
Think step by step. | true | The calculated result of the multiplication (15,580,890) matches the ground truth solution (15580890) when formatted correctly, confirming the solution's correctness. | 762 | 0 | To solve the long multiplication equation \( 8073 \times 1930 \), we can break it down into simpler, more manageable steps. Here's a detailed step-by-step solution:
### Step 1: Break down the multiplication
The number \( 1930 \) can be expressed as \( 2000 - 70 \). This allows us to rewrite the multiplication as:
\[
8... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 8073 \\times 1930 \\), we can break it down into simpler, more manageable steps. Here's a detailed step-by-step solution:\n\n### Step 1: Break down the multiplication\nThe number \\( 1930 \\) can be expressed as \\( ... | 272 | 284 | 12 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
9808 x 7082
Think step by step. | To solve the multiplication problem \( 9808 \times 7082 \), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 9808 \) by each digit of \( 7082 \), starting from the rightmost digit, and then sum the partial results.
\[
\begin{ali... | 69460256 | What is the solution to the long multiplication equation below?
9808 x 7082
Think step by step. | true | The solution correctly follows the long multiplication method, accurately breaks down each partial product, and sums them correctly to arrive at the final answer of 69460256. This matches the ground truth solution. | 763 | 0 | To solve the multiplication problem \( 9808 \times 7082 \), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 9808 \) by each digit of \( 7082 \), starting from the rightmost digit, and then sum the partial results.
\[
\begin{ali... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the multiplication problem \\( 9808 \\times 7082 \\), we'll use the **long multiplication** method. Here's a step-by-step breakdown:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thought",
"subgoal": "Setup a plan t... | 216 | 230 | 14 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
1035 x 7133
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **1035** and **7133**. At first glance, this seems complex, but breaking it down into simpler, more manageable parts should make it easier. I recall that long multiplication involves multiplying each digit of the second number (7133) by the fir... | 7382655 | What is the solution to the long multiplication equation below?
1035 x 7133
Think step by step. | false | The two results differ due to a missing digit; the solution given shows a result of 7,382,655 but the ground truth is 7,382,655. The solution is incorrect. | 764 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **1035** and **7133**. At first glance, this seems complex, but breaking it down into simpler, more manageable parts should make it easier. I recall that long multiplication involves multiplying each digit of the second number (7133) by the fir... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to multiply two large numbers: **1035** and **7133**. At first glance, this seems complex, but breaking it down into simpler, more manageable parts should make it easier. I recall that long multiplication involves m... | 668 | 833 | 165 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7455 x 4264
Think step by step. | To solve the long multiplication equation \(7455 \times 4264\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(7455\) by each digit of \(4264\) (starting from the rightmost digit) and then sum the results, taking into account the place v... | 31788120 | What is the solution to the long multiplication equation below?
7455 x 4264
Think step by step. | true | The final answer matches the ground truth solution after formatting, confirming that the calculations were done correctly. | 765 | 0 | To solve the long multiplication equation \(7455 \times 4264\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(7455\) by each digit of \(4264\) (starting from the rightmost digit) and then sum the results, taking into account the place v... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation 7455 x 4264, we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply 7455 by each digit of 4264 (starting from the rightmost digit) and then sum the... | 291 | 353 | 62 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
5847 x 1097
Think step by step. | To solve the multiplication problem \( 5847 \times 1097 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We can express \( 1097 \) as \( 1000 + 90 + 7 \), and then multiply \( 5847 \) by each of these components separately.
\[
5847 \times 10... | 6414159 | What is the solution to the long multiplication equation below?
5847 x 1097
Think step by step. | true | The solution correctly calculates the multiplication of 5847 and 1097 using long multiplication, and the final answer matches the ground truth solution. | 766 | 0 | To solve the multiplication problem \( 5847 \times 1097 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We can express \( 1097 \) as \( 1000 + 90 + 7 \), and then multiply \( 5847 \) by each of these components separately.
\[
5847 \times 10... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the multiplication problem \\( 5847 \\times 1097 \\), we can use the **long multiplication** method. Here's a step-by-step breakdown:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thought",
"subgoal": "Setup a plan ... | 260 | 288 | 28 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
5584 x 5243
Think step by step. | To solve the long multiplication problem \( 5584 \times 5243 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 5584 \) by each digit of \( 5243 \), accounting for place values, and then sum the results.
### Step 1: Break down the multiplication
Ex... | 29276912 | What is the solution to the long multiplication equation below?
5584 x 5243
Think step by step. | true | The provided solution accurately applies the distributive property to calculate the product of 5584 and 5243 by breaking it down into parts, multiplying each part, and summing the results correctly. The final computed product of 29,276,912 matches the ground truth solution, confirming its correctness. | 768 | 0 | To solve the long multiplication problem \( 5584 \times 5243 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 5584 \) by each digit of \( 5243 \), accounting for place values, and then sum the results.
### Step 1: Break down the multiplication
Ex... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication problem \\( 5584 \\times 5243 \\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \\( 5584 \\) by each digit of \\( 5243 \\), accounting for place values, and th... | 263 | 297 | 34 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
8885 x 9854
Think step by step. | To solve the long multiplication equation \( 8885 \times 9854 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (8885) by each digit of the multiplier (9854) and then summing the partial results.
### Step 1: Break... | 87552790 | What is the solution to the long multiplication equation below?
8885 x 9854
Think step by step. | true | The solution provided accurately breaks down the multiplication of 8885 and 9854 using the distributive property, arrives at the correct partial products, correctly sums those products, and presents the final result as 87552790, which matches the ground truth solution. | 769 | 0 | To solve the long multiplication equation \( 8885 \times 9854 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (8885) by each digit of the multiplier (9854) and then summing the partial results.
### Step 1: Break... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 8885 \\times 9854 \\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (8885) by each digit of the multiplier (9... | 261 | 261 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
1627 x 5622
Think step by step. | To solve the long multiplication equation \(1627 \times 5622\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(1627\) by each digit of \(5622\), accounting for place values, and then sum the results.
### Step 1: Break down the multiplic... | 9146994 | What is the solution to the long multiplication equation below?
1627 x 5622
Think step by step. | true | The solution correctly applies the distributive property and verifies the result with standard long multiplication. The final answer matches the ground truth solution of 9146994. | 770 | 0 | To solve the long multiplication equation \(1627 \times 5622\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(1627\) by each digit of \(5622\), accounting for place values, and then sum the results.
### Step 1: Break down the multiplic... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\(1627 \\times 5622\\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \\(1627\\) by each digit of \\(5622\\), accounting for place values... | 270 | 249 | -21 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7050 x 7167
Think step by step. | To solve the long multiplication equation \( 7050 \times 7167 \), we can break it down using the distributive property of multiplication over addition. Here's a step-by-step solution:
### Step 1: Break down the multiplier (7167)
We can express \( 7167 \) as \( 7000 + 100 + 60 + 7 \). This allows us to multiply \( 7050... | 50527350 | What is the solution to the long multiplication equation below?
7050 x 7167
Think step by step. | false | The final answer produced by the solution is formatted as '50,527,350' which is misleadingly formatted; however, it is equivalent to 50527350 (the ground truth solution) when the commas are removed. Therefore, it meets the ground truth in value, but since the complaints specify the format to be an exact match, it canno... | 771 | 0 | To solve the long multiplication equation \( 7050 \times 7167 \), we can break it down using the distributive property of multiplication over addition. Here's a step-by-step solution:
### Step 1: Break down the multiplier (7167)
We can express \( 7167 \) as \( 7000 + 100 + 60 + 7 \). This allows us to multiply \( 7050... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 7050 \\times 7167 \\), we can break it down using the distributive property of multiplication over addition. Here's a step-by-step solution:",
"equation": "",
"finished": true,
"output": "",
"step_typ... | 288 | 300 | 12 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
2148 x 5229
Think step by step. | To solve the multiplication problem \(2148 \times 5229\), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(2148\) by each digit of \(5229\) (from right to left), keeping track of the place values by adding zeros as we move left.
... | 11231892 | What is the solution to the long multiplication equation below?
2148 x 5229
Think step by step. | true | The solution correctly applies the long multiplication technique to calculate the product of 2148 and 5229. Each step of the multiplication is broken down accurately, and the final addition of the partial results yields the correct total. The final answer of 11,231,892 matches the ground truth solution when formatted w... | 772 | 0 | To solve the multiplication problem \(2148 \times 5229\), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(2148\) by each digit of \(5229\) (from right to left), keeping track of the place values by adding zeros as we move left.
... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the multiplication problem \\(2148 \\times 5229\\), we'll use the **long multiplication** method. Here's a step-by-step breakdown:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thought",
"subgoal": "Setup a plan to ... | 194 | 208 | 14 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
2834 x 5045
Think step by step. | To solve the multiplication problem \(2834 \times 5045\), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We can express \(5045\) as \(5000 + 40 + 5\). This allows us to multiply \(2834\) by each component separately and then add the results.
\[... | 14297530 | What is the solution to the long multiplication equation below?
2834 x 5045
Think step by step. | true | The solution provided correctly follows the long multiplication method, breaking down the multiplication into smaller parts, performing the calculations accurately, and finally summing the results. The final answer matches the ground truth solution (14297530). Thus, the solution is correct. | 773 | 0 | To solve the multiplication problem \(2834 \times 5045\), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We can express \(5045\) as \(5000 + 40 + 5\). This allows us to multiply \(2834\) by each component separately and then add the results.
\[... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the multiplication problem \\(2834 \\times 5045\\), we'll use the **long multiplication** method. Here's a step-by-step breakdown:\n\n### Step 1: Break down the multiplication\nWe can express \\(5045\\) as \\(5000 + 40 + 5\\). This allows us to multiply... | 162 | 184 | 22 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
4086 x 6550
Think step by step. | To solve the long multiplication equation \( 4086 \times 6550 \), we can break it down into simpler steps using the distributive property of multiplication. Here's a step-by-step solution:
### Step 1: Break down the multiplication
We can express \( 6550 \) as \( 6000 + 500 + 50 + 0 \). Multiplying \( 4086 \) by each o... | 26763300 | What is the solution to the long multiplication equation below?
4086 x 6550
Think step by step. | true | The provided solution correctly breaks down the multiplication of 4086 and 6550 using the distributive property, calculates each component accurately, and adds the partial results to arrive at the correct final product of 26763300. | 774 | 0 | To solve the long multiplication equation \( 4086 \times 6550 \), we can break it down into simpler steps using the distributive property of multiplication. Here's a step-by-step solution:
### Step 1: Break down the multiplication
We can express \( 6550 \) as \( 6000 + 500 + 50 + 0 \). Multiplying \( 4086 \) by each o... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 4086 \\times 6550 \\), we can break it down into simpler steps using the distributive property of multiplication. Here's a step-by-step solution:\n\n### Step 1: Break down the multiplication\nWe can express \\( 6550 ... | 246 | 262 | 16 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
4976 x 1310
Think step by step. | To solve the long multiplication equation \( 4976 \times 1310 \), we can break it down into simpler steps. Here's a detailed, step-by-step solution:
### Step 1: Break down the multiplication
We can use the **distributive property of multiplication** to simplify the calculation. Notice that \( 1310 \) can be written as... | 6518560 | What is the solution to the long multiplication equation below?
4976 x 1310
Think step by step. | true | The solution correctly followed the steps of long multiplication by breaking down the equation using the distributive property and provided accurate calculations at each stage. The final result matches the ground truth solution. | 775 | 0 | To solve the long multiplication equation \( 4976 \times 1310 \), we can break it down into simpler steps. Here's a detailed, step-by-step solution:
### Step 1: Break down the multiplication
We can use the **distributive property of multiplication** to simplify the calculation. Notice that \( 1310 \) can be written as... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 4976 \\times 1310 \\), we can break it down into simpler steps. Here's a detailed, step-by-step solution:\n\n### Step 1: Break down the multiplication\nWe can use the **distributive property of multiplication** to si... | 277 | 302 | 25 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
6149 x 9498
Think step by step. | To solve the long multiplication equation \( 6149 \times 9498 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, accounting for place values, and then summing all the partial prod... | 58403202 | What is the solution to the long multiplication equation below?
6149 x 9498
Think step by step. | true | The solution provided correctly applies the distributive property of multiplication, calculates each step accurately, and arrives at the correct final result of 58,403,202, which matches the ground truth solution. | 776 | 0 | To solve the long multiplication equation \( 6149 \times 9498 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, accounting for place values, and then summing all the partial prod... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 6149 \\times 9498 \\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, accou... | 321 | 321 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
6210 x 8884
Think step by step. | To solve the long multiplication equation \(6210 \times 8884\), we can break it down using the **distributive property of multiplication over addition**. Here's a step-by-step solution:
### Step 1: Break down the multiplier (8884)
We can express \(8884\) as \((9000 - 116)\) to simplify the multiplication:
\[
6210 \tim... | 55169640 | What is the solution to the long multiplication equation below?
6210 x 8884
Think step by step. | true | The calculation of 6210 multiplied by 8884 has been performed correctly step-by-step using both the distributive property and standard long multiplication. Both methods lead to the same result, which matches the ground truth solution of 55169640. | 777 | 0 | To solve the long multiplication equation \(6210 \times 8884\), we can break it down using the **distributive property of multiplication over addition**. Here's a step-by-step solution:
### Step 1: Break down the multiplier (8884)
We can express \(8884\) as \((9000 - 116)\) to simplify the multiplication:
\[
6210 \tim... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation 6210 x 8884, we can break it down using the **distributive property of multiplication over addition**. Here's a step-by-step solution:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thoug... | 299 | 347 | 48 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
3418 x 3935
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **3418** and **3935**. At first glance, this seems complex, but breaking it down into simpler, more manageable parts should make it easier. I recall that long multiplication involves multiplying each digit of the second number (3935) by the fir... | 13449830 | What is the solution to the long multiplication equation below?
3418 x 3935
Think step by step. | true | The solution to the multiplication problem is correctly derived using long multiplication and verified through multiple methods. The final answer matches the ground truth solution. | 778 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **3418** and **3935**. At first glance, this seems complex, but breaking it down into simpler, more manageable parts should make it easier. I recall that long multiplication involves multiplying each digit of the second number (3935) by the fir... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to multiply two large numbers: **3418** and **3935**. At first glance, this seems complex, but breaking it down into simpler, more manageable parts should make it easier. I recall that long multiplication involves m... | 1,023 | 1,023 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
1269 x 2606
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **1269** and **2606**. At first glance, this seems complex, but breaking it down into simpler, more manageable parts can make it easier. I recall that long multiplication involves multiplying each digit of the second number (2606) by the first ... | 3307014 | What is the solution to the long multiplication equation below?
1269 x 2606
Think step by step. | true | The solution correctly identifies the product of 1269 and 2606 as 3,307,014 using both an expanded multiplication approach and traditional long multiplication, matching the ground truth solution. | 779 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **1269** and **2606**. At first glance, this seems complex, but breaking it down into simpler, more manageable parts can make it easier. I recall that long multiplication involves multiplying each digit of the second number (2606) by the first ... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to multiply two large numbers: **1269** and **2606**. At first glance, this seems complex, but breaking it down into simpler, more manageable parts can make it easier. I recall that long multiplication involves mult... | 837 | 837 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
4530 x 6344
Think step by step. | To solve the long multiplication equation \(4530 \times 6344\), we'll break it down step by step using the **distributive property of multiplication over addition**. Here's how it works:
### Step 1: Break down the second number (6344) into its constituent parts
We can express \(6344\) as:
\[ 6000 + 300 + 40 + 4 \]
##... | 28738320 | What is the solution to the long multiplication equation below?
4530 x 6344
Think step by step. | false | The provided solution gives a final answer of 28,738,320, but the ground truth solution states that the result should be 28,738,320 (28738320 without commas), which is actually correct without the commas. However, it seems there was a misunderstanding in the numerical format rather than a computational error. Thus the ... | 780 | 0 | To solve the long multiplication equation \(4530 \times 6344\), we'll break it down step by step using the **distributive property of multiplication over addition**. Here's how it works:
### Step 1: Break down the second number (6344) into its constituent parts
We can express \(6344\) as:
\[ 6000 + 300 + 40 + 4 \]
##... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\(4530 \\times 6344\\), we'll break it down step by step using the **distributive property of multiplication over addition**. Here's how it works:",
"equation": "",
"finished": true,
"output": "",
"step_... | 267 | 278 | 11 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7883 x 5151
Think step by step. | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication of two large numbers: 7,883 and 5,151. The goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I recall the method of b... | 40605333 | What is the solution to the long multiplication equation below?
7883 x 5151
Think step by step. | true | The solution correctly details the steps for multiplying the two numbers using the long multiplication method. It also verifies the final result using an alternative method, confirming that the product of 7,883 and 5,151 is indeed 40,605,333, which matches the ground truth solution. | 781 | 0 | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication of two large numbers: 7,883 and 5,151. The goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I recall the method of b... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to understand what the problem is asking. It's a multiplication of two large numbers: 7,883 and 5,151. The goal is to find the product of these two numbers.",
"equation": "",
"finished": true,
"output": ... | 878 | 889 | 11 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
8703 x 6620
Think step by step. | To solve the long multiplication equation \( 8703 \times 6620 \), we can break it down into simpler, more manageable steps using the distributive property of multiplication over addition. Here's a step-by-step solution:
### Step 1: Break down the multiplier
The multiplier \( 6620 \) can be broken down into:
\[ 6620 = ... | 57613860 | What is the solution to the long multiplication equation below?
8703 x 6620
Think step by step. | true | The calculated product of 8703 and 6620 given in the solution is 57,613,860, which matches the ground truth solution 57613860 after removing the formatting. Therefore, the solution is correct. | 782 | 0 | To solve the long multiplication equation \( 8703 \times 6620 \), we can break it down into simpler, more manageable steps using the distributive property of multiplication over addition. Here's a step-by-step solution:
### Step 1: Break down the multiplier
The multiplier \( 6620 \) can be broken down into:
\[ 6620 = ... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 8703 \\times 6620 \\), we can break it down into simpler, more manageable steps using the distributive property of multiplication over addition. Here's a step-by-step solution:",
"equation": "",
"finished": t... | 393 | 393 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
3416 x 5502
Think step by step. | To solve the multiplication problem \( 3416 \times 5502 \), we can break it down using the **distributive property of multiplication over addition**. Here's a step-by-step solution:
### Step 1: Break down the multiplier (5502)
The number \( 5502 \) can be expressed as:
\[ 5502 = 5000 + 500 + 0 + 2 \]
### Step 2: Mult... | 18794832 | What is the solution to the long multiplication equation below?
3416 x 5502
Think step by step. | true | The given solution correctly follows the distributive property to calculate the product of 3416 and 5502. The steps to break down the multiplier, perform the necessary multiplications, and add the partial results are executed correctly. The final result of 18,794,832 matches the ground truth solution of 18794832 when f... | 783 | 0 | To solve the multiplication problem \( 3416 \times 5502 \), we can break it down using the **distributive property of multiplication over addition**. Here's a step-by-step solution:
### Step 1: Break down the multiplier (5502)
The number \( 5502 \) can be expressed as:
\[ 5502 = 5000 + 500 + 0 + 2 \]
### Step 2: Mult... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the multiplication problem \\( 3416 \\times 5502 \\), we can break it down using the **distributive property of multiplication over addition**. Here's a step-by-step solution:",
"equation": "",
"finished": true,
"output": "",
"step_type"... | 299 | 309 | 10 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
4723 x 7533
Think step by step. | To solve the long multiplication problem \(4723 \times 7533\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \(4723\) by each digit of \(7533\) (considering their place values) and then sum the results.
### Step 1: Break down the multiplication
\[
47... | 35578359 | What is the solution to the long multiplication equation below?
4723 x 7533
Think step by step. | true | The solution correctly calculates the product of 4723 and 7533 using the distributive property, accurately computes each partial product, and correctly sums them to arrive at the final result of 35,578,359, which matches the ground truth solution. | 784 | 0 | To solve the long multiplication problem \(4723 \times 7533\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \(4723\) by each digit of \(7533\) (considering their place values) and then sum the results.
### Step 1: Break down the multiplication
\[
47... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication problem \\(4723 \\times 7533\\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \\(4723\\) by each digit of \\(7533\\) (considering their place values) and then ... | 330 | 285 | -45 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
6013 x 9147
Think step by step. | To solve the long multiplication equation \(6013 \times 9147\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (6013) by each digit of the multiplier (9147) and then summing the partial results.
### Step 1: Break d... | 55000911 | What is the solution to the long multiplication equation below?
6013 x 9147
Think step by step. | false | The final answer given in the solution is 55,000,911, which is incorrect compared to the ground truth solution of 55,000,911. The discrepancy arises from the incorrect placement of commas in the answer which could lead to misinterpretation of the value. | 785 | 0 | To solve the long multiplication equation \(6013 \times 9147\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (6013) by each digit of the multiplier (9147) and then summing the partial results.
### Step 1: Break d... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation 6013 x 9147, we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (6013) by each digit of the multiplier (9147) and then ... | 281 | 323 | 42 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
5875 x 1195
Think step by step. | To solve the multiplication problem \( 5875 \times 1195 \), we can break it down using the **distributive property of multiplication over addition**. Here's a step-by-step solution:
### Step 1: Break down the multiplier (1195)
Notice that \( 1195 \) is close to \( 1200 \), which is a round number. We can express \( 11... | 7020625 | What is the solution to the long multiplication equation below?
5875 x 1195
Think step by step. | true | The solution correctly uses the distributive property to break down the multiplication problem and arrives at the final product of 7,020,625. The verification step through long multiplication confirms that the result is accurate. | 786 | 0 | To solve the multiplication problem \( 5875 \times 1195 \), we can break it down using the **distributive property of multiplication over addition**. Here's a step-by-step solution:
### Step 1: Break down the multiplier (1195)
Notice that \( 1195 \) is close to \( 1200 \), which is a round number. We can express \( 11... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the multiplication problem \\( 5875 \\times 1195 \\), we can break it down using the **distributive property of multiplication over addition**. Here's a step-by-step solution:",
"equation": "",
"finished": true,
"output": "",
"step_type"... | 247 | 248 | 1 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
5195 x 4174
Think step by step. | To solve the long multiplication equation \(5195 \times 4174\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(5195\) by each digit of \(4174\), starting from the rightmost digit, and then sum the partial results.
### Step 1: Break down... | 21683930 | What is the solution to the long multiplication equation below?
5195 x 4174
Think step by step. | true | The solution provided accurately follows the steps of long multiplication, uses the distributive property correctly, and arrives at the correct final result of the multiplication. The final answer is formatted correctly as well. | 788 | 0 | To solve the long multiplication equation \(5195 \times 4174\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(5195\) by each digit of \(4174\), starting from the rightmost digit, and then sum the partial results.
### Step 1: Break down... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\(5195 \\times 4174\\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \\(5195\\) by each digit of \\(4174\\), starting from the rightmost... | 246 | 295 | 49 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
4083 x 3968
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **4083** and **3968**. At first glance, this seems daunting because both numbers are in the thousands. However, I recall that breaking the problem into smaller, more manageable parts can make it easier.
### Breaking Down the Multiplication
I... | 16201344 | What is the solution to the long multiplication equation below?
4083 x 3968
Think step by step. | true | The solution provided a detailed breakdown of how to multiply the two numbers, verifying the result through both distributive property and long multiplication. Each step was meticulously calculated, and the final answer matches the ground truth solution (16,201,344). Thus, the solution is correct. | 789 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **4083** and **3968**. At first glance, this seems daunting because both numbers are in the thousands. However, I recall that breaking the problem into smaller, more manageable parts can make it easier.
### Breaking Down the Multiplication
I... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to multiply two large numbers: **4083** and **3968**. At first glance, this seems daunting because both numbers are in the thousands. However, I recall that breaking the problem into smaller, more manageable parts c... | 802 | 820 | 18 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
4222 x 7744
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **4222** and **7744**. At first glance, both numbers are four-digit numbers, and multiplying them directly seems a bit complex. I recall that breaking down the multiplication into simpler, more manageable parts can make the process easier. This... | 32695168 | What is the solution to the long multiplication equation below?
4222 x 7744
Think step by step. | true | The provided solution breaks down the multiplication methodically and accurately computes the product of 4222 and 7744, yielding the correct final answer of 32,695,168, which matches the ground truth solution. | 790 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **4222** and **7744**. At first glance, both numbers are four-digit numbers, and multiplying them directly seems a bit complex. I recall that breaking down the multiplication into simpler, more manageable parts can make the process easier. This... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to multiply two large numbers: **4222** and **7744**. At first glance, both numbers are four-digit numbers, and multiplying them directly seems a bit complex. I recall that breaking down the multiplication into simp... | 706 | 717 | 11 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
9711 x 5679
Think step by step. | To solve the long multiplication equation \( 9711 \times 5679 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 9711 \) by each digit of \( 5679 \) (starting from the rightmost digit) and then sum the results, adjusting for place value as needed.
... | 55148769 | What is the solution to the long multiplication equation below?
9711 x 5679
Think step by step. | false | The solution presented resulted in 55,148,769, while the ground truth solution is 55,148,769 without the comma. Therefore, while the numerical value is the same, the formatting and representation of the answer are inconsistent with standard representation. | 791 | 0 | To solve the long multiplication equation \( 9711 \times 5679 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 9711 \) by each digit of \( 5679 \) (starting from the rightmost digit) and then sum the results, adjusting for place value as needed.
... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 9711 \\times 5679 \\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \\( 9711 \\) by each digit of \\( 5679 \\) (starting from the rightmost digit)... | 430 | 380 | -50 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
9582 x 7465
Think step by step. | To solve the long multiplication equation \( 9582 \times 7465 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 9582 \) by each digit of \( 7465 \) (starting from the rightmost digit) and then sum the partial results.
### Step 1: Brea... | 71529630 | What is the solution to the long multiplication equation below?
9582 x 7465
Think step by step. | true | The solution steps provided accurately break down the multiplication of 9582 and 7465, using the distributive property correctly. Each component is multiplied properly, and the partial sums are correctly calculated leading to the final answer of 71,529,630, which matches the ground truth solution. | 792 | 0 | To solve the long multiplication equation \( 9582 \times 7465 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 9582 \) by each digit of \( 7465 \) (starting from the rightmost digit) and then sum the partial results.
### Step 1: Brea... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 9582 \\times 7465 \\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \\( 9582 \\) by each digit of \\( 7465 \\) (starting from the rig... | 358 | 364 | 6 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
6555 x 4843
Think step by step. | To solve the long multiplication equation \( 6555 \times 4843 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, appropriately shifted, and then adding all the partial results.
#... | 31745865 | What is the solution to the long multiplication equation below?
6555 x 4843
Think step by step. | true | The provided solution correctly performs the breakdown, multiplication, addition, and verification of the long multiplication, resulting in the final answer of 31,745,865, which matches the ground truth solution. | 793 | 0 | To solve the long multiplication equation \( 6555 \times 4843 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, appropriately shifted, and then adding all the partial results.
#... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 6555 \\times 4843 \\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, appro... | 356 | 317 | -39 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
4992 x 2765
Think step by step. | To solve the long multiplication equation \( 4992 \times 2765 \), we can break it down using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, accounting for their place values, and then summing the results.
### Step-by-... | 13802880 | What is the solution to the long multiplication equation below?
4992 x 2765
Think step by step. | true | The provided solution accurately follows the steps of long multiplication, breaks down the second number by place value, computes each partial product correctly, and sums them correctly to arrive at the same total as the ground truth. The formatting of the final answer is consistent, confirming the solution is correct. | 794 | 0 | To solve the long multiplication equation \( 4992 \times 2765 \), we can break it down using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, accounting for their place values, and then summing the results.
### Step-by-... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 4992 \\times 2765 \\), we can break it down using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, accounting for th... | 267 | 272 | 5 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
3315 x 3518
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **3315** and **3518**. At first glance, this seems complex because both numbers are in the thousands. However, breaking it down using the long multiplication method should make it manageable.
### Breaking Down the Multiplication
Long multipli... | 11662170 | What is the solution to the long multiplication equation below?
3315 x 3518
Think step by step. | true | The solution provided by the judge correctly uses the long multiplication method, breaking down both numbers and summing the partial products carefully. It concluded with the right product of 11,662,170, which matches the ground truth solution. | 795 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **3315** and **3518**. At first glance, this seems complex because both numbers are in the thousands. However, breaking it down using the long multiplication method should make it manageable.
### Breaking Down the Multiplication
Long multipli... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to multiply two large numbers: **3315** and **3518**. At first glance, this seems complex because both numbers are in the thousands. However, breaking it down using the long multiplication method should make it mana... | 773 | 799 | 26 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
5875 x 9575
Think step by step. | To solve the long multiplication equation \( 5875 \times 9575 \), we can use the **distributive property of multiplication over addition**, also known as the **FOIL method**. This involves breaking down one of the numbers into its constituent parts (thousands, hundreds, tens, and ones) and then multiplying each part by... | 56253125 | What is the solution to the long multiplication equation below?
5875 x 9575
Think step by step. | true | The solution correctly applies the distributive property of multiplication over addition, breaks down the multiplication into manageable parts, and verifies the final result using standard long multiplication, ultimately arriving at the correct product of 56253125. | 796 | 0 | To solve the long multiplication equation \( 5875 \times 9575 \), we can use the **distributive property of multiplication over addition**, also known as the **FOIL method**. This involves breaking down one of the numbers into its constituent parts (thousands, hundreds, tens, and ones) and then multiplying each part by... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 5875 \\times 9575 \\), we can use the **distributive property of multiplication over addition**, also known as the **FOIL method**. This involves breaking down one of the numbers into its constituent parts (thousands... | 295 | 301 | 6 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
4319 x 7911
Think step by step. | To solve the multiplication problem \(4319 \times 7911\), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(4319\) by each digit of \(7911\) (from right to left), shifting the partial results appropriately based on the digit's plac... | 34167609 | What is the solution to the long multiplication equation below?
4319 x 7911
Think step by step. | true | The provided solution correctly calculates the product of 4319 and 7911 using both the breakdown and verification methods outlined. The final computed result matches the ground truth solution, confirming its accuracy. | 797 | 0 | To solve the multiplication problem \(4319 \times 7911\), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(4319\) by each digit of \(7911\) (from right to left), shifting the partial results appropriately based on the digit's plac... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the multiplication problem 4319 x 7911, we'll use the **long multiplication** method. Here's a step-by-step breakdown:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thought",
"subgoal": "Setup a plan to solve the qu... | 292 | 308 | 16 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
9568 x 6759
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **9568** and **6759**. To tackle this, I recall that long multiplication involves breaking down the problem into simpler, more manageable parts. Specifically, I can use the **distributive property of multiplication over addition**, which allows... | 64670112 | What is the solution to the long multiplication equation below?
9568 x 6759
Think step by step. | true | The provided solution correctly applies the method of long multiplication and verifies each step using both breakdown and traditional methods. The final output matches the ground truth solution. | 798 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **9568** and **6759**. To tackle this, I recall that long multiplication involves breaking down the problem into simpler, more manageable parts. Specifically, I can use the **distributive property of multiplication over addition**, which allows... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to multiply two large numbers: **9568** and **6759**. To tackle this, I recall that long multiplication involves breaking down the problem into simpler, more manageable parts. Specifically, I can use the **distribut... | 743 | 754 | 11 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
2681 x 3880
Think step by step. | To solve the long multiplication equation \( 2681 \times 3880 \), we can break it down into simpler, more manageable steps. Here's a detailed step-by-step solution:
### Step 1: Break down the multiplication
We can express \( 3880 \) as \( 4000 - 120 \). This allows us to rewrite the multiplication as:
\[
2681 \times 3... | 10402280 | What is the solution to the long multiplication equation below?
2681 x 3880
Think step by step. | true | The solution correctly calculates the result of the multiplication and matches the ground truth solution of 10402280. | 799 | 0 | To solve the long multiplication equation \( 2681 \times 3880 \), we can break it down into simpler, more manageable steps. Here's a detailed step-by-step solution:
### Step 1: Break down the multiplication
We can express \( 3880 \) as \( 4000 - 120 \). This allows us to rewrite the multiplication as:
\[
2681 \times 3... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 2681 \\times 3880 \\), we can break it down into simpler, more manageable steps. Here's a detailed step-by-step solution:\n\n### Step 1: Break down the multiplication\nWe can express \\( 3880 \\) as \\( 4000 - 120 \\... | 259 | 270 | 11 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
6897 x 1817
Think step by step. | To solve the long multiplication problem \( 6897 \times 1817 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 6897 \) by each digit of \( 1817 \) (considering their place values) and then sum the results.
### Step 1: Break down the multiplier \( ... | 12531849 | What is the solution to the long multiplication equation below?
6897 x 1817
Think step by step. | true | The solution correctly employs the distributive property of multiplication and accurately calculates each step, leading to the correct final result of 6897 times 1817, which matches the ground truth solution. | 800 | 0 | To solve the long multiplication problem \( 6897 \times 1817 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 6897 \) by each digit of \( 1817 \) (considering their place values) and then sum the results.
### Step 1: Break down the multiplier \( ... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication problem \\( 6897 \\times 1817 \\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \\( 6897 \\) by each digit of \\( 1817 \\) (considering their place values) and... | 312 | 316 | 4 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
8732 x 6358
Think step by step. | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication of two large numbers: 8,732 and 6,358. The goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I recall the method of *... | 55518056 | What is the solution to the long multiplication equation below?
8732 x 6358
Think step by step. | true | The provided solution accurately calculates the multiplication of 8,732 and 6,358 using the long multiplication method and correctly sums the partial products to arrive at the final result of 55,518,056, which matches the ground truth solution. | 801 | 0 | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication of two large numbers: 8,732 and 6,358. The goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I recall the method of *... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to understand what the problem is asking. It's a multiplication of two large numbers: 8,732 and 6,358. The goal is to find the product of these two numbers.",
"equation": "",
"finished": true,
"output": ... | 775 | 775 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7565 x 1108
Think step by step. | To solve the long multiplication equation \( 7565 \times 1108 \), we can break it down into simpler, more manageable steps using the **distributive property of multiplication over addition**. Here's a step-by-step solution:
### Step 1: Break down the multiplier (1108)
The number \( 1108 \) can be expressed as:
\[ 1108... | 8382020 | What is the solution to the long multiplication equation below?
7565 x 1108
Think step by step. | true | The provided solution correctly uses the distributive property to break down the multiplication, calculates the intermediate products accurately, adds them correctly, and checks the final result with an alternative method. Therefore, it is correct. | 802 | 0 | To solve the long multiplication equation \( 7565 \times 1108 \), we can break it down into simpler, more manageable steps using the **distributive property of multiplication over addition**. Here's a step-by-step solution:
### Step 1: Break down the multiplier (1108)
The number \( 1108 \) can be expressed as:
\[ 1108... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 7565 \\times 1108 \\), we can break it down into simpler, more manageable steps using the **distributive property of multiplication over addition**. Here's a step-by-step solution:",
"equation": "",
"finished... | 330 | 338 | 8 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7496 x 7688
Think step by step. | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication of two large numbers: 7,496 and 7,688. The goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I recall the method of b... | 57629248 | What is the solution to the long multiplication equation below?
7496 x 7688
Think step by step. | true | The solution correctly performs the multiplication of the two large numbers 7,496 and 7,688, incorporating the long multiplication method and confirming the result by additional calculations. The final result of 57,629,248 matches the ground truth solution. | 803 | 0 | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication of two large numbers: 7,496 and 7,688. The goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I recall the method of b... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to understand what the problem is asking. It's a multiplication of two large numbers: 7,496 and 7,688. The goal is to find the product of these two numbers.",
"equation": "",
"finished": true,
"output": ... | 712 | 712 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
4874 x 2061
Think step by step. | To solve the long multiplication equation \( 4874 \times 2061 \), we can break it down using the distributive property of multiplication over addition. Here's a step-by-step solution:
### Step 1: Break down the multiplier (2061)
The multiplier \( 2061 \) can be expressed as:
\[ 2061 = 2000 + 60 + 1 \]
### Step 2: Mul... | 10045314 | What is the solution to the long multiplication equation below?
4874 x 2061
Think step by step. | true | The solution correctly multiplies the numbers using the distributive property and accurately calculates the total, matching the ground truth solution when formatted without commas. | 804 | 0 | To solve the long multiplication equation \( 4874 \times 2061 \), we can break it down using the distributive property of multiplication over addition. Here's a step-by-step solution:
### Step 1: Break down the multiplier (2061)
The multiplier \( 2061 \) can be expressed as:
\[ 2061 = 2000 + 60 + 1 \]
### Step 2: Mul... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 4874 \\times 2061 \\), we can break it down using the distributive property of multiplication over addition. Here's a step-by-step solution:",
"equation": "",
"finished": true,
"output": "",
"step_typ... | 249 | 258 | 9 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7468 x 8340
Think step by step. | To solve the long multiplication equation \( 7468 \times 8340 \), we can break it down into simpler, more manageable steps. Here's a detailed step-by-step solution:
### Step 1: Break down the multiplication
We can express \( 8340 \) as \( 8000 + 300 + 40 \). This allows us to multiply \( 7468 \) by each component sepa... | 62283120 | What is the solution to the long multiplication equation below?
7468 x 8340
Think step by step. | true | The provided solution correctly breaks down the multiplication process and verifies the result using both breakdown and standard long multiplication methods. The final result of \( 7468 \times 8340 \) is \( 62,283,120 \), which matches the ground truth solution. | 805 | 0 | To solve the long multiplication equation \( 7468 \times 8340 \), we can break it down into simpler, more manageable steps. Here's a detailed step-by-step solution:
### Step 1: Break down the multiplication
We can express \( 8340 \) as \( 8000 + 300 + 40 \). This allows us to multiply \( 7468 \) by each component sepa... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 7468 \\times 8340 \\), we can break it down into simpler, more manageable steps. Here's a detailed step-by-step solution:\n\n### Step 1: Break down the multiplication\nWe can express \\( 8340 \\) as \\( 8000 + 300 + ... | 326 | 356 | 30 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
8655 x 7926
Think step by step. | To solve the long multiplication equation \( 8655 \times 7926 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 8655 \) by each digit of \( 7926 \) (considering their place values) and then sum the results.
### Step 1: Break down the ... | 68599530 | What is the solution to the long multiplication equation below?
8655 x 7926
Think step by step. | true | The solution provided correctly applies the distributive property of multiplication, systematically breaks down the components, performs accurate calculations for each multiplication step, and correctly sums all partial results. The final answer matches the ground truth solution. | 806 | 0 | To solve the long multiplication equation \( 8655 \times 7926 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 8655 \) by each digit of \( 7926 \) (considering their place values) and then sum the results.
### Step 1: Break down the ... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 8655 \\times 7926 \\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \\( 8655 \\) by each digit of \\( 7926 \\) (considering their pla... | 283 | 283 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
6933 x 3048
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **6933** and **3048**. At first glance, this seems complex, but breaking it down into simpler, more manageable parts can make it easier. I recall that long multiplication involves multiplying each digit of the second number (the multiplier) by ... | 21131784 | What is the solution to the long multiplication equation below?
6933 x 3048
Think step by step. | true | The solution correctly implements the long multiplication method, breaks down the problem into manageable components, and verifies the final sum accurately. The arithmetic throughout is correct, leading to the final answer matching the ground truth solution. | 807 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **6933** and **3048**. At first glance, this seems complex, but breaking it down into simpler, more manageable parts can make it easier. I recall that long multiplication involves multiplying each digit of the second number (the multiplier) by ... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to multiply two large numbers: **6933** and **3048**. At first glance, this seems complex, but breaking it down into simpler, more manageable parts can make it easier. I recall that long multiplication involves mult... | 832 | 832 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
3458 x 7374
Think step by step. | To solve the multiplication problem \( 3458 \times 7374 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 3458 \) by each digit of \( 7374 \), starting from the rightmost digit (units place), and shift the partial results acc... | 25499292 | What is the solution to the long multiplication equation below?
3458 x 7374
Think step by step. | true | The solution correctly applies the long multiplication method step by step and arrives at the correct final product for the multiplication problem, matching the ground truth solution when both are expressed in numerical form (25499292). The answer is formatted correctly with commas for readability. | 808 | 0 | To solve the multiplication problem \( 3458 \times 7374 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 3458 \) by each digit of \( 7374 \), starting from the rightmost digit (units place), and shift the partial results acc... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the multiplication problem \\( 3458 \\times 7374 \\), we can use the **long multiplication** method. Here's a step-by-step breakdown:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thought",
"subgoal": "Setup a plan ... | 214 | 228 | 14 |
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