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.
Case study _unit2.8.1 Example 1: Finding 17% of 80
Method
17% of 80 = of 80, so here we do:
Extract _unit2.8.1
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:
Extract _unit2.8.2
17 × 80 = 1360
1360 ÷ 100 = 13.6
The answer will be the same.
Case study _unit2.8.2 Example 2: Finding 3% of £52.24
Method
3% of 52.24 = of 52.24, so we do:
Extract _unit2.8.3
52.24 ÷ 100 = 0.5224.
0.5224 × 3 = £1.5672 (£ 1.57 to two d.p.)
Or
Extract _unit2.8.4
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%.
Box _unit2.8.2 10%
To find 10% of an amount divide by 10:
Extract _unit2.8.5
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.
Box _unit2.8.3 1%
To find 1% of an amount divide by 100:
Extract _unit2.8.6
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.
Case study _unit2.8.3 Example 1: Finding 24% of 60
Find 10% first:
Extract _unit2.8.7
60 ÷ 10 = 6
10% = 6
20% is 2 lots of 10% so:
Extract _unit2.8.8
6 × 2 = 12
20% = 12
Now find 1%:
Extract _unit2.8.9
60 ÷ 100 = 0.6
4% is 4 lots of 1% so:
Extract _unit2.8.10
0.6 × 4 = 2.4
4% = 2.4
Now add the 20% and 4% together:
12 + 2.4 = 14.4
Case study _unit2.8.4 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:
Extract _unit2.8.11
328 ÷ 10 = 32.8
10% = 32.8
5% is half of the 10% so:
Extract _unit2.8.12
32.8 ÷ 2 = 16.4
5% = 16.4
2.5% is half of the 5% so:
Extract _unit2.8.13
16.4 ÷ 2 = 8.2
2.5% = 8.2
Now add the 10%, 5% and 2.5% figures together:
Extract _unit2.8.14
32.8 + 16.4 + 8.2 = £57.40
This is a good method to do in stages when you do not have a calculator.
Box _unit2.8.4
Note: There are some other quick ways of working out certain percentages:
Extract _unit2.8.15
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 _unit2.8.1 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 _unit2.8.2 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.