Percentages · Grade 8
In Grade 8 you learn: reverse percentages.
Per cent means “out of 100”, so 35% means 35 out of every 100. Percentages make it easy to compare discounts, test scores, interest rates and survey results, even when the totals are different.
Key facts
- 50% = a half, 25% = a quarter, 10% = ÷ 10, 1% = ÷ 100.
- Build other percentages from these: 35% = 10% + 10% + 10% + 5%.
- With a calculator: p% of an amount = p ÷ 100 × amount (17.5% of 64 = 0.175 × 64 = 11.2).
- To write A as a percentage of B: A ÷ B × 100. Put both in the same units first.
- Working backwards: if 30% is 42, then 1% is 1.4 and 100% is 140.
- The percentages that make up a whole add up to 100%.
Worked examples
Example 1
A coat costing £64 is reduced by 15% in a sale. What is the sale price?
Answer: £54.40
Example 2
40% of a number is 46. What is the number?
Answer: 115