# 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 50100
We can simplify 50100 by dividing the top and bottom by 50
50100 = 12

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

10% is the same as 10100
We can simplify 10100 by dividing the top and bottom by 10
10100 = 110

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

1% is the same as 1100

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

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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

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## 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 3332, we can press the SD button to get a decimal answer: 3332 = 166.5

### Converting to a decimal or a fraction

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 1892, we can press the SD button to get a decimal answer: 1892 = 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% = 55100
9% = 9100
87% = 87100
29% = 29100
17.5% = 17.5100

Example 9: Work out 82% of 125

82% = 82100

We type 82100 × 125 into the calculator:            This gives an answer of 2052, we can press the SD button to get a decimal answer: 2052 = 102.5

Try these: