Year 6AC9M6N07

Percentages of Quantities

Solve problems that require finding a familiar fraction, decimal or percentage of a quantity, including percentage discounts, choosing efficient calculation strategies.

Read this first

Find 10% first. Everything else builds from there.

30 shaded out of 100 is 30%. Notice it is three lots of 10%.

Words you need

Per cent: Out of 100.
Quantity: The whole amount you are finding a percentage of.

Worked example

e.g. Find 30% of 250.

Find 10% first. To do that, divide by 10. $250 \div 10 = 25$ .
You want 30%, which is three lots of 10%.
$25 \times 3 = 75$ .
So 30% of 250 is 75.

10% is the building block. Halve it for 5%, double it for 20%, treble it for 30%. Most questions fall out from there.

Practice

The pictures fade as you go. By the last few you are on your own.

1What percentage is shaded?with a picture

Answer20%.

2Find 20% of 60.with a hint

Need a hint?

Find 10% first, then double it.

Answer12. 10% is 6, so 20% is 12.

3Find 15% of 80.with a hint

Need a hint?

10% is 8. Half of that is 5%. Add them.

Answer12.

8 + 4 = 12

4Find 10% of 340.on your own

Answer34.

5Find 40% of 150.on your own

Answer60.

6Find 5% of 200.on your own

Answer10.

7A jacket costs

\$60

. You get 25% off. How much comes off the price?on your own

Answer

\$15

. A quarter of 60 is 15.

8There are 300 children at a school. 60% walk to school. How many walk?on your own

Answer180. 10% is 30, and

30 \times 6 = 180

Think about it

Why is finding 10% so useful?

One good answerIt is just dividing by 10, which is quick. Every other percentage can be built from it by doubling, halving or adding.

Is 50% of 80 the same as 80% of 50?

One good answerYes, both are 40. Swapping the percentage and the amount gives the same answer every time, which can make a hard sum easy.

30% of a number is 45. How could you find the whole number?

One good answerIf 30% is 45, then 10% is 15. The whole is 100%, which is ten lots of 10%, so

15 \times 10 = 150

Common mistakes

Dividing by the percentage instead of finding 10% first.

For 30% of 250, do not divide by 30. Find 10%, then take three of them.

Giving the discount when the question asks for the price.

Read it again. 25% off

\$60

means

\$15

comes off, so you pay

\$45

Thinking a percentage is a fixed amount.

10% of 50 is 5, but 10% of 500 is 50. It always depends on the whole.