Stage 10 · Percentages & speed
Using percentages
Whole × the %; up 10% is × 110%.
How to do it
Method
Whole × the %; up 10% is × 110%
50 up 10%: 50 × 110% = 55
Another way
Find the increase first
50 × 10% = 5, 50 + 5 = 55
In full
A percentage is a fraction out of 100. A percentage of an amount: the whole × the percentage, times then ÷ 100: 35% of a class of 40 → 40 × 35 = 1400, 1400 ÷ 100 = 14 pupils. What percentage one number is of another: part ÷ whole × 100%: 14 of 40 is 14 ÷ 40 × 100% = 35%. Up by a percentage: the number × (100% + the increase): 50 up 10% → 50 × 110% = 55; down by one: the number × (100% − the decrease): 50 down 10% → 50 × 90% = 45. In Hong Kong shops 八折 means you pay 80% of the price, that is 20% off; 七五折 is 75% of the price: $200 at 八折 → 200 × 80% = $160. Or find the increase or decrease first, then add it or take it away: 50 × 10% = 5, 50 + 5 = 55 — the same answer.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
$800, 50% off: $?
Show the answer and working
Answer: $800, 50% off: $400
50% off leaves 50% of the price: 800 × 50 = 40000, 40000 ÷ 100 = 400
Example 2
Glasses: 90% of 20 pupils = ?
Show the answer and working
Answer: Glasses: 90% of 20 pupils = 18
90% of 20: 20 × 90%, 20 × 90 = 1800, 1800 ÷ 100 = 18
Example 3
Orange: 135 of 150 trees = ?%
Show the answer and working
Answer: Orange: 135 of 150 trees = 90%
135 ÷ 150 × 100%: 135 × 100 = 13500, 13500 ÷ 150 = 90, so 90%
Example 4
80 increased by 30% = ?
Show the answer and working
Answer: 80 increased by 30% = 104
Up 30% leaves 100% + 30% = 130% of the number: 80 × 130 = 10400, 10400 ÷ 100 = 104
Practise using percentages in the game →Stage 10 · Percentages & speed · Free to start, unlimited questions, no download