Per cent means out of a hundred. 17 out of 20 and 41 out of 50 become 85 and 82, and the comparison takes a second.
The three conversions
| From | To | What to do |
|---|---|---|
| Fraction | Percentage | Multiply by 100: 3/4 × 100 = 75% |
| Percentage | Fraction | Put it over 100 and reduce: 75/100 = 3/4 |
| Decimal | Percentage | Move the point two places right: 0.75 becomes 75% |
Moving the point two places is not a separate rule. Multiplying by a hundred moves every digit two columns left. So 1.25 is 125 per cent, which is perfectly legal.
Find ten per cent by moving the point one place, then build what you need. Ten per cent of 800 is 80, five per cent is 40, so fifteen per cent is 120.
Percentage increase and decrease
Change divided by the ORIGINAL amount, times a hundred. 400 to 460 is a change of 60, and 60 over 400 is 15 per cent.
100 rises 20% to 120. A 20% fall is then calculated on 120, not 100, so it removes 24 and leaves 96. The two percentages were taken from different starting points.
60% of 20 girls and 50% of 40 boys is not 55%. Count the people: 12 and 20 passed, which is 32 out of 60, about 53%.
After a 20% discount, 720 is 80% of the original, not 100%. One per cent is 9, so the original was 900. Adding 20% back onto 720 gives the wrong answer.
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