How to multiply fractions, with a recipe example

A pancake recipe needs 3/4 cup of milk. For half a batch, use half that milk: 3/8 cup. Multiplying fractions lets you resize a recipe, even when the starting amount is already a fraction.

Half the recipe, half the milk

Both bars show one cup divided into eight equal parts. The full recipe needs six parts. Half the recipe needs three.

Full recipe: 3/4 cup = 6/8 cup

Half recipe: 3/8 cup

Work out the milk for half a batch

What is half of 3/4 cup?

Multiply the top numbers

$1\times3=3$

This gives the top number of the answer.
Multiply the bottom numbers

$2\times4=8$

This gives the bottom number. Put the two results together as one fraction.
Put the answer back into the recipe

$\frac12\times\frac34=\frac38\text{ cup}$

Use 3/8 cup of milk for half a batch. The picture shows half as much milk as the full recipe.

Why the pieces become eighths

Each quarter of a cup becomes an eighth when you take half. You started with three of those pieces, so you end with three eighths. That is why the bottom number changes from four to eight.

Multiplication can make an amount smaller

Multiplying by 1/2 takes half an amount. It does not double it. Here, the milk drops from 3/4 cup to 3/8 cup. A fraction between zero and one tells you to take part of what you started with.

Need two batches instead? Use 2 × 3/4 = 6/4, or 1½ cups. The same method scales a recipe up or down.

You can simplify an answer by dividing its top and bottom by the same number. For example, 6/8 becomes 3/4 when you divide both by two. Both fractions name the same amount.

Try it yourself

Work out an answer and explain your reasoning. Then check the explanation.

Make a different batch size

$\frac23\times\frac34$

A full batch needs 3/4 cup of milk. How much milk do you need for two thirds of a batch?

Show the answerHide the answer

$\frac12\text{ cup}$

Multiply the tops to get six and the bottoms to get twelve. The answer is 6/12 cup, or 1/2 cup.

Fix a wrong answer

$\frac12\times\frac34=\frac36$

Someone adds the bottom numbers instead of multiplying them. Correct the calculation for half a batch.

Show the answerHide the answer

$\frac38\text{ cup}$

Multiply the bottoms, 2 × 4 = 8. Do not add them. Half a batch needs 3/8 cup of milk.

Shortcut: simplify before you multiply

For (1/6) × (6/7), multiplying gives 6/42. Divide the top and bottom by six to get 1/7.

You can do that division first. Divide the top six and the bottom six by six; each becomes one. Then (1/1) × (1/7) = 1/7. Cancelling first keeps the numbers small.

Use this shortcut when multiplying, not adding. In 1/6 + 6/7, crossing out the sixes would change the amounts you are adding.

Divide a top and bottom by the same number

Both sixes become one when you divide them by six. The answer stays one seventh.

Try multiplying new fractions

Multiply the tops and bottoms, then simplify if you can. Try a few questions to check that you can use the method with new numbers.

2-minute practice · keep going after mistakes · opens in a new tab

Try fraction multiplication