Multiplying and dividing fractions
Maths · Key Stage 2 · The School
Multiplying two fractions
To multiply two fractions, multiply the tops together, then multiply the bottoms together. One half times two thirds: multiply the tops, 1 times 2, to get 2. Multiply the bottoms, 2 times 3, to get 6. The answer is two sixths, which simplifies to one third. No common bottom number is needed first. That is one thing that makes multiplying fractions easier than adding them.
Why the answer gets smaller
This can feel backwards, because multiplying whole numbers usually makes a number bigger. But finding a fraction OF a fraction means taking a smaller piece of an already small piece. One half of two thirds is smaller than two thirds. Multiplying fractions shrinks the amount, and that is the correct, expected result. Picture cutting an already small slice of cake in half again. The new piece is smaller still.
Dividing a fraction by a whole number
To divide a fraction by a whole number, multiply the bottom by that number instead, and leave the top alone. One third divided by 2: multiply the bottom, 3 times 2, to get 6. The top stays 1. The answer is one sixth — a smaller piece, split further. Dividing a fraction always shrinks it further still. Sharing an already small piece between more people leaves everyone with even less.
A real problem, solved
A recipe uses three quarters of a bag of sugar, shared equally between 3 cakes. Divide three quarters by 3. Multiply the bottom: 4 times 3 makes 12. The top stays 3. That gives three twelfths, which simplifies to one quarter. Each cake gets one quarter of the whole bag.