Number (Intermediate) - Percentages
 
Understanding Percentages | Finding a Percentage | Increasing or Decreasing by a Percentage
Writing an Amount as a Percentage
 

Understanding Percentages

Percentages are fractions with a denominator of 100.

For example,
 50 percent (50%) = 50/100 = 1/2
  20 percent (20%) = 20/100 = 1/5

Changing a fraction or decimal to a percentage - simply multiply by 100.

Examples: ½ x 100 = 50
so
 ½ = 50%
  ¼ x 100 = 25
so
 ¼ = 25%
  1/3 x 100 = 33
 1
3
so
 1
3
 = 33
1
3
 %
  0.35 x 100 = 35
so
 0.35 = 35%
  0.625 x 100 = 62.5
so
 0.625 = 62.5%

Changing a percentage to a decimal or fraction — simply divide by 100.

Examples:

28% = 28/100 = 7/25
 
 

75% = 75/100 = ¾
 
 

28% = 28/100 = 0.28
 
 

75% = 75/100 = 0.25

 

Finding a Percentage of a Quantity

Example1: Work out 25% of 40.

Method: Write 25% as a fraction and then multiply by 40.

  25% of 40
 =
25
100
 x 40
    =
 ¼ x 40
    =
 10


Example 2: Calculate 50% of 60.

    =
50
100
 x 60
    =
 ½ x 60
    =
 30
  

Note: for the non-calculator paper, 10% is an easy percentage to use.

10% = 10/100 =1/10 so 10% of a quantity is simply one tenth, which can be worked out by dividing by 10.

 

10% of 30 = 30 ÷ 10 = 3

10% of 80 = 8

10% of 250 = 25

10% of 16 = 1.6

10% of 38 = 3.8

We can use this to work out other percentages:

 

 20% of 30
 = 3 x 2 = 6 (simply double the 10%)
  30% of 30
 = 3 x 3 = 9 (multiply the 10% by 3)
  15% of 30
 = 10% of 30 + 5% of 30
 
= 3 + 1.5
    = 4.5
Using this method we can work out any percentage which is a multiple of 10 or 5, without using a calculator.

 

Increasing or Decreasing by a Percentage

Example 1: Increase £40 by 8%.

Method: work out the 8% and add it on.

  8% of 40
 = 8/100 of 40
    = 40 ÷ 100 x 8
    = 3.2 (calculator method)

So, 8% of 40 = £3.20 (note: calculator will give 3.2, but this must be written as £3.20 for money)

Now add this on to 40 to give £43.20

OR

Work out (100 + 8)% of 40
 = 108% of 40
  = 108/100 of 40
  = 40 ÷ 100 x108 (on calculator)
  = £43.20

Example 2: Decrease £40 by 8%.

In this case we subtract the 8%.

£40 – 3.20 = £36.80

OR

100 – 8 = 92 so 92% of 40 = £36.80 (giving the answer directly)


Example 3: In a sale, all prices are reduced by 30%. What is the sale price of a coat costing £80 before the sale?

Reduction = 30% of 80 = £24

Sale price = 80 – 24 = £56

 

Writing an Amount as a Percentage

This is the same thing as writing as a fraction, then changing it to a percentage.

Example 1: I score 18 out of 20 in a test. What is this as a percentage?

 
Fraction
=
 18/20
 
18/20 x 100
=
 100 ÷ 20 x 18
   
=
 90
 
So, 18/20
=
 90%

Example 2: I have 40 sweets and I eat 8. What fraction have I eaten?

 
8/40
=
 20%
What percentage do I have left?

 
100 – 20
=
 80 so I have 80% left.

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