# 8.1 Calculating a percentage of an amount

## Method 1

Percentages are just fractions where the number on the bottom of the fraction must be 100. If you wanted to find out 15% of 80 for example, you work out of 80, which you already know how to do!

Working out the percentage of an amount requires a similar method to finding the fraction of an amount. Take a look at the examples below to increase your confidence.

### Example 1: Finding 17% of 80

#### Method

17% of 80 = of 80, so here we do:

80 ÷ 100 = 0.8

0.8 × 17 = 13.6

Another way of thinking about this method is that you are dividing by 100 to find 1% first and then you are multiplying by whatever percentage you want to find.

Alternatively, you could multiply the value by the top number first and then divide by 100:

17 × 80 = 1360

1360 ÷ 100 = 13.6

The answer will be the same.

### Example 2: Finding 3% of £52.24

#### Method

3% of 52.24 = of 52.24, so we do:

52.24 ÷ 100 = 0.5224.

0.5224 × 3 = £1.5672 (£ 1.57 to two d.p.)

Or

52.24 × 3 = 156.72

156.72 ÷ 100 = £1.5672 (£1.57 to two d.p.)

This is a good method if you want to be able to work out every percentage in the same way. It can be used with and without a calculator. Many calculators have a percentage key, but different calculators work in different ways so you need to familiarise yourself with how to use the % button on your calculator.

## Method 2

To use this method you only need to be able to work out 10% and 1% of an amount. You can then work out any other percentage from these.

Let’s just recap how to find 10% and 1%.

### 10%

To find 10% of an amount divide by 10:

10% of £765 = 765 ÷ 10 = £76.50

10% of £34.50 = 34.50 ÷ 10 = £3.45

*Hint: remember to move the decimal point one place to the left to divide by 10. *

### 1%

To find 1% of an amount divide by 100:

1% of £765 = 765 ÷ 100 = £7.65

1% of £34.50 = 34.50 ÷ 100 = £0.345 (£0.35 to two d.p.)

*Hint: remember to move the decimal point two places to the left to divide by 100. *

Once you know how to work out 10% and 1%, you can work out any other percentage.

## Example 1: Finding 24% of 60

Find 10% first:

60 ÷ 10 = 6

10% = 6

20% is 2 lots of 10% so:

6 × 2 = 12

**20% = 12**

Now find 1%:

60 ÷ 100 = 0.6

4% is 4 lots of 1% so:

0.6 × 4 = 2.4

**4% = 2.4**

Now add the 20% and 4% together:

12 + 2.4 = 14.4

## Example 2: Finding 17.5% of £328

17.5% can be broken up into 10% + 5% + 2.5%, so you need to work out each of these percentages and then add them together.

Find 10% first:

328 ÷ 10 = 32.8

**10% = 32.8**

5% is half of the 10% so:

32.8 ÷ 2 = 16.4

**5% = 16.4**

2.5% is half of the 5% so:

16.4 ÷ 2 = 8.2

**2.5% = 8.2**

Now add the 10%, 5% and 2.5% figures together:

32.8 + 16.4 + 8.2 = £57.40

This is a good method to do in stages when you do not have a calculator.

**Note**: There are some other quick ways of working out certain percentages:

50% – divide the amount by two.

25% – halve and halve again.

These quick facts can be used in combination with method 2 to make calculations, e.g. 60% could be worked out by finding 50%, 10% and then adding the 2 figures together. You just need to look for the easiest way to split up the percentage to make your calculation.

## Activity 17: Finding percentages of amounts

Use whichever method/s you prefer to calculate the answers to the following:

Find:

a.45% of £125

b.15% of 455 m

c.52% of £677

d.16% of £24.50

e.2% of 4000 kg

f.82% of £7.25

g.37% of £95

The Cambria Bank pays interest at 3.5%. What is the interest on £3000?

Sure Insurance offer a 30% No Claims Bonus. How much would be saved on a premium of £345.50?

Sunshine Travel Agents charge 1.5% commission on foreign exchanges. What is the charge for changing £871?

### Answer

a.£56.25

b.68.25 m

c.£352.04

d.£3.92

e.100 kg

f.£5.945 (£5.95 to 2 d.p.)

g.£35.625 (£35.63 to two d.p.)

£105

£103.65

£13.065 (£13.07 to two d.p.)

Just as with fractions you will often need to be able to work out the price of an item after it has been increased or decreased by a given percentage. The process for this is the same as with fractions; you simply work out the percentage of the amount and then add it to, or subtract it from, the original amount.

## Activity 18: Percentages increase and decrease

You earn £500 per month. You get a 5% pay rise.

a.How much does your pay increase by?

b.How much do you now earn per month?

### Answer

a.£25

b.£525 per month.

You buy a new car for £9500. By the end of the year its value has decreased by 20%.

a.How much has the value of the car decreased by?

b.How much is the car worth now?

### Answer

a.The car has decreased by £1900.

b.The car is now worth £7600.

You invest £800 in a building society account which offers fixed-rate interest at 4% per year.

a.How much interest do you earn in one year?

b.How much do you have in your account at the end of the year?

### Answer

a.£32 interest earned.

b.£832 in the account at the end of the year.

Last year Julie’s car insurance was £356 per annum. This year she will pay 12% less. How much will she pay this year?

### Answer

She will pay £42.72 less so her insurance will cost £313.28

A zoo membership is advertised for £135 per year. If Tracy pays for the membership in full rather than in monthly installments, she receives a 6% discount. How much will she pay if she pays in full?

### Answer

She will save £8.10 so she will pay £126.90.

A museum had approximately 5.87 million visitors last year. Visitor numbers are expected to increase by 4% this year. How many visitors is the museum expecting this year?

### Answer

5.87 million = 5 870 000.

4% of 5 870 000 = 234 800

5 870 000 + 234 800 = 6 104 800 people

Next you’ll look at how to express one number as a percentage of another.