Year 7AC9M7N06

Finding a Percentage of a Quantity

Use the 4 operations with positive rational numbers including fractions, decimals and percentages to solve problems using efficient calculation strategies.

There are two ways to do this: a calculator method and a mental method. Learn both, because the mental one is faster in half the questions you will meet.

Builds onYr 7 · Fractions, Decimals and Percentages

Method

‘Of’ means multiply

15\% \text{ of } 80 = 0{,}15 \times 80

Turn the percentage into a decimal, then multiply.

10% is the useful building block

10\% = \div 10

From 10% you can reach 5%, 20%, 30% and 1% quickly.

1% is dividing by 100

Handy for awkward percentages like 3% or 7%.

Estimate to check

15% of 80 must be less than a quarter of 80, so under 20.

Worked example

e.g.

\text{Find } 15\% \text{ of } 80

Calculator method. Write the percentage as a decimal. $15\% = 0{,}15$
Multiply by the amount. $0{,}15 \times 80 = 12$
Mental method. Start by finding 10%. $10\% \text{ of } 80 = 8$
Halve that to get 5%. $5\% \text{ of } 80 = 4$
Add the parts you need. $10\% + 5\% = 8 + 4 = 12$
Both methods agree, and the answer is under 20 as expected. $15\% \text{ of } 80 = 12 \quad\checkmark$

Practice

Try the mental method first, then check with the decimal method.

25\% \text{ of } 60

Answer

15

30\% \text{ of } 150

Answer

45

5\% \text{ of } 240

Answer

12

12{,}5\% \text{ of } 64

Answer

8

\text{A jacket costs } 90. \text{ Find } 20\% \text{ of it.}

Answer

18

\text{Explain how to find } 35\% \text{ using only } 10\% \text{ and } 5\%

Answer

3 \times 10\% + 5\%