Working out 1/2 × 3/2 = 3/4, Neha notices 3/4 is bigger than 1/2

Why

Neha's calculation is actually completely correct — 1 × 3 = 3 on top, 2 × 2 = 4 on the bottom, giving exactly 3/4, and 3/4 truly is bigger than 1/2. What's worth catching is the rule she's applying too broadly. Multiplying by a fraction shrinks the result only when that fraction is smaller than 1 — a 'proper' fraction like 1/3 or 1/4. But 3/2 is an IMPROPER fraction: its top number is bigger than its bottom, which means 3/2 is actually bigger than 1 (it equals one-and-a-half). Multiplying by something bigger than 1 grows a number, exactly as multiplying by 2 or 3 would, whether that 'something bigger than 1' is written as a whole number or as a fraction. So the shrink-rule only applies to a slice of all possible fractions, not fractions in general. Test: 1/2 × 5/4 = 5/8, and 5/8 is again bigger than 1/2, because 5/4 (one-and-a-quarter) is bigger than 1 too — the pattern holds every time the multiplying fraction exceeds 1. No, 1/2 × 3/2 = 3/4 is correct: multiplying by a fraction bigger than 1 grows the result, and 'multiplying by any fraction shrinks it' is only true for fractions smaller than 1, not fractions in general.