Multiplication and Division of Fractions

The Story

"Multiplying fractions is actually the EASY operation," said Ms. Rao. "No common denominator needed at all. Just multiply straight across: numerator times numerator, denominator times denominator." For 2/3 x 3/4: numerators 2x3=6, denominators 3x4=12, giving 6/12, which simplifies to 1/2.

"Now division," said Ms. Rao, writing 1/2 ÷ 1/4. "Dividing by a fraction uses a trick: flip the SECOND fraction upside down (find its reciprocal), then multiply instead of divide." 1/4 flipped is 4/1. So 1/2 ÷ 1/4 becomes 1/2 x 4/1 = 4/2 = 2. "Dividing by 1/4 asks 'how many quarters fit into a half?' — and the answer, 2, makes perfect sense: two quarters make a half."

Kabir tried another: 2/3 ÷ 1/6. Flip 1/6 to get 6/1. Multiply: 2/3 x 6/1 = 12/3 = 4. "How many sixths fit into two-thirds?" he checked — two-thirds equals four-sixths, and four sixths obviously contains four separate sixths. "The trick actually matches what the question is really asking."

"Remember this difference," said Ms. Rao. "Multiplication: straight across, no flipping. Division: flip the second fraction, THEN multiply straight across. Mixing up which operation needs the flip is the single most common mistake — always double-check which one you're doing before reaching for the reciprocal."