## The Lesson

Fractions can be divided. Imagine you wanted to divide^{1}/

_{5}(one-fifth) by

^{2}/

_{3}(two-thirds).

## How to Divide Fractions

## Question

Divide the fractions below.**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).# 2

Change the ÷ sign to a × sign.

^{1}/

_{5}(one-fifth) by

^{3}/

_{2}.

# 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.# 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}

## 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:The operation becomes...

...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:

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: