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Class 8 Fractions in Disguise: cheat sheet
CBSE Mathematics. A percentage is a fraction with denominator 100. Find a percentage of a quantity, convert between forms, and work out increases, decreases and proportions.
Key ideas
- x% means x/100: 25% = 1/4 = 0.25.
- To write a fraction as a percentage, multiply it by 100%.
- Percentage change is always worked out on the original value.
- An increase of r% multiplies by (1 + r/100); a decrease multiplies by (1 − r/100).
- A rise of 10% followed by a fall of 10% does not bring you back to the start.
- Four numbers are in proportion when the product of the outer two equals the product of the middle two.
Remember
| Percentage of a quantity | x% of Q = x × Q ÷ 100 |
| Percentage change | change ÷ original × 100% |
| After a change | new = original × (100 ± r) ÷ 100 |
| Proportion | a : b = c : d ⇔ a × d = b × c |
Watch out
- Dividing the change by the new value instead of the original.
- Adding percentages of different totals as if they were the same.
- Comparing the wrong products when testing for a proportion.
Worked example
Are 5, 30, 7 and 43 in proportion? Give a reason.
Working: product of extremes 5 × 43 = 215; product of means 30 × 7 = 210
Answer: No
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