# Finding the percentage of a quantity

It's often useful to be able to find a percentage of a quantity. For example, you might be told that bus fares are going up by and you need to know how much more you will need to pay each week.

Here are a couple of ways you could do it:

## Method 1

Find of the quantity by dividing it by .

Find of a quantity by multiplying of the quantity by .

To find of a quantity you need to multiply of the quantity by .

Question

Rakesh has a box containing pens. of the pens are red.

How many red pens does the box contain?

You need to find of .

of is

So of is

## Method 2

Find the percentage of a quantity by multiplying that quantity by the percentage expressed as a fraction.

This combines the division and multiplication of Method 1 into one sum.

Question

Q1. In a class of pupils, live in a flat. How many pupils live in a flat?

Q2. Last year Sam earned . This year her pay has increased by .

a) By how much money has Sam's pay increased?

b) What is her new salary?

A1. is equivalent to

of

Therefore pupils live in a flat.

A2.

a) Method 1:

of

of

b) Method 2:

So Sam's new salary is:

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