Maths

Percentages

'Percent' means 'out of 100'. If 90 per cent of the population owns a mobile phone, this means 90 out of every 100 people have one. The symbol '%' means per cent.

A percentage is a fraction of 100.

**30%** (30 in each 100) as a fraction is ^{30}/_{100}

**30%** as a decimal is **0.3**.

Often, in real life - and maths exams - you must find a percentage of a quantity. First, write the percentage as a fraction or a decimal, then multiply by the quantity.

Have a look at this question:

- Question
Find 40% of £50.

- Answer
First, write 40% as a fraction: 40% =

^{40}/_{100}=^{4}/_{10}=^{2}/_{5}Now multiply by the quantity:

^{2}/_{5}× 50 =**£20.**

Practise converting percentages to fractions. Then try the questions below.

- Question
Sarah is buying a pair of jeans. The original price was £75, but there is a discount of 30%. How much will the discount be?

- Answer
Discount = 30% of 75

=

^{30}/_{100}× 75= 0.3 × 75

= £22.50

Note that if the question asked for the discount price, you would subtract the discount from the original price : £75 - £22.50 = £52.50.

Sometimes both the percentage and amount of money will not be whole numbers.

- Question
A car costs £9,999.90 before VAT (value added tax). Work out the cost of the VAT if it is charged at 20%.

- Answer
VAT = 20% of £9,999.90

= 20/100 × 9,999.90

= 1,999.98

Since the answer is a price, it must be rounded to two decimal places.

The answer is

**£1,999.98**

People pay tax on the income they earn. The basic rate of income tax is 20% (as of 2011).

Value Added Tax is added to the cost of most things you buy. It is charged at 20% (as of 2011).

In some questions you are given the cost price and the selling prices and have to find the percentage increase or decrease. This means you need to find one amount as a percentage of another. You form a fraction from the two amounts and multiply this by 100. Try these questions.

With **simple interest** the amount of money borrowed remains fixed.

For example £400 is borrowed for 3 years at an interest rate of 5% pa (pa means **per annum**, or each year).

Interest for one year = 5% of £400

= (^{5}/_{100} ) × 400

= **£20**

Interest for 3 years = £20 × 3 = **£60**.

You can write this in a formula.

**Interest = P × R × T**

- P (principal) is the amount borrowed.
- R is the rate of interest per year.
- T is the time in years.

People often buy something at one price, and sell it on for another - eg, when they are selling things at a car boot sale.

If the selling price is greater than the buying price, a **profit** is made.

If the selling price is less than the buying price, there is a **loss**.

- Question
Ajay is dealing in electrical goods. He buys a radio for £45 and sells it for £63. What is his percentage profit?

- Answer
Here the cost price is £45 and the selling price £63.

The profit is £63 - £45 = £18

To calculate the percentage profit you have to find what the profit is as a percentage of the original price. So divide the profit by the original price and multiply by 100.

18 ÷ 45 x 100 =

**40%**.

- Question
Charlotte buys a coat in a sale for £60. The original cost of the coat was £80. What is the percentage decrease?

- Answer
The coat was bought for £60, and the original price was £80.

The decrease is £80 - £60 = £20.

To calculate the percentage decrease, divide the actual decrease by the original price and multiply by 100.

20 ÷ 80 x 100 =

**25%**.

**Now try a **Test Bite