Percentages · Usually met around P6
Percentage increase and decrease
Work on the original: up p% means × (100 + p)%.
How to do it
Method
Work on the original: up p% means × (100 + p)%
80 up 15%: 80 × 115100 = 92
Another way
Find the change first
80 × 15100 = 12, 80 + 12 = 92
In full
A percentage increase or decrease is always worked out on the original number (the one before the change). Way 1, in one step: after an increase of p% you have (100 + p)% of the original, so 80 up 15% → 80 × 115100 = 92; after a decrease of p% you have (100 − p)% left, so 80 down 15% → 80 × 85100 = 68. Way 2, find the change first, then add it or take it away: 80 × 15100 = 12, 80 + 12 = 92, 80 − 12 = 68, the same. Going back to the percentage change: change ÷ original × 100%; from 80 to 92 is up 12, and 12 ÷ 80 × 100% = 15%. Careful: divide by the original, not the new number; and up 20% then down 20% doesn't get you back, since the second change is worked out on a bigger number: 100 → 120 → 96.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
A number goes up from 400 to 520. By what percentage has it increased?
Show the answer and working
Answer: 30%
It went up by 520 − 400 = 120; divide by the original: 120 ÷ 400 × 100% = 30%.
Example 2
840 is decreased by 15%. Which calculation gives the result?
- A. 840 − 15
- B. 840 × 1.15
- C. 840 × 0.15
- D. 840 × 0.85
Choose the right answer
Show the answer and working
Answer: D. 840 × 0.85
Down 15% leaves 100% − 15%, which is 0.85: 840 × 0.85.
Example 3
Increase 100 by 10%, then decrease the result by 10%. The final result is □.
Show the answer and working
Answer: 99
Up first: 100 × (100 + 10)/100 = 110; then down from 110: 110 × (100 − 10)/100 = 99. The second 10% is taken from a bigger number, so it doesn't get back to 100.
Practise it in the game →Percentages · Free to start, unlimited questions, no download