Percentages

Finding a Percentage of an Amount without a calculator

Percent means out of 100

When we work out percentages without a calculator we usually start by working out 50%, 10% or 1%.

50% is the same as 50⁄100
We can simplify 50⁄100 by dividing the top and bottom by 50
50⁄100 = 1⁄2

We work out 50% of a number by halving it.

10% is the same as 10⁄100
We can simplify 10⁄100 by dividing the top and bottom by 10
10⁄100 = 1⁄10

We work out 10% of a number by dividing it by 10.

1% is the same as 1⁄100

We work out 1% of a number by dividing it by 100.

Example 1: Work out 50% of £320

To work out 50% of an amount we divide it by 2

£320 ÷ 2 = £160
50% of 320 = £160

Example 2: Work out 10% of £320

To work out 10% of an amount we divide it by 10

£320 ÷ 10 = £32
10% of 320 = £32

Example 3: Work out 1% of £320

To work out 1% of an amount we divide it by 100

£320 ÷ 100 = £3.20
1% of 320 = £3.20

Try these:

We can use 50%, 10% and 1% to work out harder percentages.

Example 4: Work out 21% of $250

21% = 10% + 10% + 1%

We can work out 10% by dividing by 10
$250 ÷ 10 = $25

We can work out 1% by dividing by 100
$250 ÷ 100 = $2.50

21% of $250 = $25 + $25 + $2.50 = $52.50

Example 5: Work out 47% of 350g

47% = 50% - 1% - 1% - 1% = 50% - 3%

We can work out 50% of 350g by halving it.
350g ÷ 2 = 175g

We can work out 1% of 350g by dividing it by 100
350g ÷ 100 = 3.5g

We can work out 3% by multiplying 1% by 3
3% of 350g = 3.5g × 3 = 10.5g

47% of 350g = 175g − 10.5g = 164.5g

Example 6: Work out 85% of £400

85% = 100% − 10% − 5%

We can work out 10% of £400 by dividing £400 by 10
£400 ÷ 10 = £40

5% is half of 10%
We can work out 5% of £400 by dividing £40 by 2
£40 ÷ 2 = £20

100% of £400 = £400

85% of £400 = £400 − £40 − £20 = £340

Try these:

Finding a Percentage of an Amount with a calculator

We can also use a calculator to work out a percentage of an amount.

We can either use the percentage button or convert the percentage to a decimal or fraction first.

Using the percentage button

On the Classwiz calculator to get % press SHIFT then the ANS button:

Example 7: Work out 37% of 450

On the calculator we type 37% × 450:

This gives an answer of 333⁄2, we can press the SD button to get a decimal answer:

333⁄2 = 166.5

Converting to a decimal or a fraction

We can convert percentages to decimals or fractions.

To convert a percentage to a decimal we divide by 100

54% = 0.54
7% = 0.07
84% = 0.84
59% = 0.59

Example 8: Work out 27% of 350

27 ÷ 100 = 0.27
27% = 0.27

We type 0.27 × 350 into the calculator:

This gives an answer of 189⁄2, we can press the SD button to get a decimal answer:

189⁄2 = 94.5

A percentage is the same as a fraction out of 100, we can We can convert percentages to fractions. by writing them over 100

55% = 55⁄100
9% = 9⁄100
87% = 87⁄100
29% = 29⁄100
17.5% = 17.5⁄100

Example 9: Work out 82% of 125

82% = 82⁄100

We type 82⁄100 × 125 into the calculator:

This gives an answer of 205⁄2, we can press the SD button to get a decimal answer:

205⁄2 = 102.5

Try these: