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Dividing Fractions

(KS2, Year 4)

Fractions can be divided. Imagine you wanted to divide 1/5 (one-fifth) by 2/3 (two-thirds). fraction_divide_example

How to Divide Fractions

Question

Divide the fractions below.
fraction divide example Dividing by a fraction can be changed to multiplying by a fraction (which is much easier!). Flip the fraction you are dividing by upside down, then change the ÷ to a ×.

Step-by-Step:

1

Flip the fraction you after the ÷ sign upside-down (so the top number becomes the bottom number and the bottom number becomes the top number).

fraction divide example step 1

2

Change the ÷ sign to a × sign.

fraction divide example step 2
Now we are multiplying fractions. Multiply 1/5 (one-fifth) by 3/2.

fraction divide example step 3+

3

Multiply the top numbers (called the numerators) of the fractions together.
1 × 3 = 3

4

Multiply the bottom numbers (called the denominators) of the fractions together.
5 × 2 = 10

5

The answer from Step 3 is the numerator of our answer. The answer from Step 4 is the denominator of our answer. fraction_divide_example_step_5

6

Simplify the fraction if possible. (The fraction in our example is already as simple as possible).

Answer:

1/5 (one-fifth) divided by 2/3 (two-thirds) equals 3/10 (three-tenths).
1/5 ÷ 2/3 = 3/10

Lesson Slides

The slider below gives a real example of how to divide fractions.

Top Tip

Dividing by a Fraction = Multiplying by the Upside-Down Fraction

Dividing by a fraction is equivalent to multiplying by the reciprocal of the fraction (i.e the fraction turned upside-down). For example, to divide by two-thirds:

divide fraction 2 mini The operation becomes...

divide fraction 3 mini ...which is just the same as multiplying fractions.

Beware

Flip the Fraction You Are Dividing by - Not Into

When dividing one fraction by another, it is very important that the fraction after the ÷ sign is flipped over, not before it. For example, to divide the following fractions:

divide fractions example mini The ÷ sign must be changed to a × sign. But it would be wrong to flip the first fraction upside-down:

divide fractions example wrong mini It would be right to flip the second fraction over:

divide fractions example right mini
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This page was written by Stephen Clarke.

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fractionsmultiplying fractionsfinding the reciprocal of a fractionfinding the power of a fraction

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