metadata
source: ncert
topic: numbers
class_level: class_7
chapter: ch9
difficulty: beginner
Class 7 | Ch9: Rational Numbers Rational: p/q where p,q integers and q≠0. Every integer=rational(n=n/1). Standard form: q>0 and HCF(p,q)=1. So -6/4=-3/2. Comparison: convert to same positive denominator, compare numerators. -3/5 vs -2/3: LCM=15 → -9/15 vs -10/15 → -3/5>-2/3. Dense: infinite rationals between any two rationals. Operations: p/q+r/s=(ps+qr)/qs. Division: (p/q)÷(r/s)=ps/qr. Finding rationals between 1/4 and 1/2: between 2/8 and 4/8 → 3/8, 5/16, 7/16. -3/5+2/3=(-9+10)/15=1/15. Denominator must be POSITIVE in standard form. -2/3 is greater than -1 (closer to zero).