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 5\% 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 1\% of the quantity by dividing it by {100}.

Find 5\% of a quantity by multiplying 1\% of the quantity by 5\%.

To find x\% of a quantity you need to multiply 1\% of the quantity by x\%.

Question

Rakesh has a box containing {60} pens. 20\% of the pens are red.

How many red pens does the box contain?

You need to find 20\% of {60}.

1\% of {60} is 60 \div 100 = 0.6

So 20\% of {60} is 0.6 \times 20 = 12

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 {25} pupils, 24\% live in a flat. How many pupils live in a flat?

Q2. Last year Sam earned \pounds{20,000}. This year her pay has increased by 8\%.

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

b) What is her new salary?

A1. 24\% is equivalent to \frac{24}{100}

24\% of 25 = \frac{24}{100} \times 25 = 6

Therefore 6 pupils live in a flat.

A2.

a) Method 1:

1\% of 20,000 = 20,000 \div 100 = 200

8\% of 20,000 = 8 \times 200 = 1,600

b) Method 2:

\frac{8}{100} \times 20,000 = 1,600

So Sam's new salary is:

\pounds{20,000} + \pounds{1,600} = \pounds{21,600}

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