## The Lesson

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

## Question

Divide the fractions below.
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 ×.

# 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).

# 2

Change the ÷ sign to a × sign.

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

# 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

# 6

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

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. Open the slider in a new tab

## 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:

The operation becomes...

...which is just the same as multiplying fractions.

## 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:

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

It would be right to flip the second fraction over: