# Multiplying and dividing fractions

**Multiplying fractions by integers**

To multiply a fraction by an integer, the following steps are carried out:

- multiply by the numerator
- divide by the denominator

For example,

Points to note:

- integer is a whole number (negative, positive or 0)
- order of division first or multiplication first will not affect the solution

In the following example, the denominator cannot be divided by 12, therefore the numerator should be multiplied first. Note that the fraction is simplified further.

**Using cancellation to simplify calculations**

When multiplying fractions, cancellation can be used if the number being multiplied by and the denominator of the fraction share a common factor. This is carried out by converting the integer into a fraction. For example,

**Multiplying a fraction by a fraction**

When multiplying two fractions together,

- multiply the numerators together
- multiply the denominators together

Note, as per the previous section, the cancellation method could also have used.

**Dividing an integer by a fraction**

When dividing by a fraction the following method is used:

- Divide by the numerator
- Multiply by the denominator

For example:

The answer is:

Point to note:

- When dividing a whole number by a fraction less than one, the result will be a larger number.

- Multiply by the denominator (5) = 20
- Divide by the numerator (2) = 10

**Dividing a fraction by a fraction**

When dividing by a fraction, multiply the denominator and divide the numerator.

- In this example, the division is changed to a multiplication by swapping the numerator and the denominator (turning the second fraction upside down).
- The multiplication step is then more straight forward as the numerators are multiplies as well as the denominators.