Multiplying and dividing fractions

Remember that to multiply fractions, you need to multiply the numerators together, and multiply the denominators together. Remember that you cannot cancel numbers that are both on the top of a fraction. Have a look at the examples below.

Example

²/₃ x ¹/₂

We multilpy ²/₃ by ¹/₂

So we have ²/₃ x ¹/₂ = ²/₆

Example

⁴/₅ x ⁵/₆

Multiply then cancel:

OR cancel between the top and the bottom then multiply:

Dividing a fraction by a whole number

Three people share ³/₄'s of a pie. They each get ¹/₄.

This means ³/₄ divided by 3 would make the answer ¹/₄.

Another way of writing 3 is ³/₁

So ³/₄ ÷ ³/₁ = ¹/₄

You get the same answer when you turn the fraction you divide by upside down, and multiply instead. For example,³/₄ x ¹/₃ = ¹/₄.

The same is true with a whole number.

15 ÷ 3 = 5 and 15 x ¹/₃ = 5

Dividing by a fraction

How do you divide 12 by ¹/₃? This isn't the same as 12 divided by 3.

12 ÷ ¹/₃ means how many thirds are there in 12 whole units.

As there are 3 thirds in each whole unit, then there are 36 thirds in 12 whole units. Think how many ¹/₃'s there are in one pie, then 12 pies.

A simple way to divide by a fraction is to turn the fraction upside down and multiply.

It works with all fractions. For example dividing by ²/₃ is the same as multiplying by ³/₂.

10 ÷ ²/₃ = ¹⁰/₁ x ³/₂ = ³⁰/₂ = ¹⁵/₁ = 15

Notice that when you divide by a fraction the answer is larger than the number you started with.

Reciprocals

The reciprocal of a number is 1 divided by that number.

Then the reciprocal of a fraction is the fraction turned upside down.

So the reciprocal of ³/₄ is ⁴/₃

For instance, to work out the reciprocal of 4:

We can think of 4 as ⁴/₁

So 4 turned upside down is ¹/₄