Fractions and percentages by hand
A fraction of an amount
Divide by the bottom number, then multiply by the top number.
- 3/8 of 240 g
- 240 ÷ 8 = 30
- 30 × 3 = 90 g
Building a percentage
Start from 10% (divide by 10).
Halve it for 5%, halve again for 2.5%, and divide by 100 for 1%. Add the pieces you need.
- 35% of 260
- 10% = 26, so 30% = 78
- 5% = 13
- 35% = 78 + 13 = 91
- 17.5% of £80
- 10% = 8, 5% = 4, 2.5% = 2
- 17.5% = 8 + 4 + 2 = 14, so £14
To increase by a percentage, work out the percentage and add it on. To decrease, take it away.
Fractions, decimals and percentages
To turn a fraction into a decimal, make the bottom 10, 100 or 1000, or divide the top by the bottom.
- 7/20
- 7/20 = 35/100
- 35/100 = 0.35 = 35%
To turn a decimal into a fraction, write it over 10, 100 or 1000, then simplify: 0.45 = 45/100 = 9/20.
To compare a mix of fractions, decimals and percentages, write them all as percentages first. 3/5 = 60%, 0.58 = 58%, so 3/5 is bigger than 0.58.
Learn a few by heart
Cover the right-hand side and say each one: 1/2 = 0.5 = 50%, 1/4 = 0.25 = 25%, 3/4 = 0.75 = 75%, 1/5 = 0.2 = 20%, 1/8 = 0.125 = 12.5%, 1/20 = 0.05 = 5%.
Most non-calculator conversions are built from these.
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