Percentages
Recognise that 100% represents the complete whole and use percentages to describe, represent and compare relative size; connect familiar percentages to their decimal and fraction equivalents.
Read this first
Per cent means out of 100. So 25% means 25 out of every 100.
There are 100 small squares. 25 are shaded. That is 25%, which is the same as one quarter.
Words you need
- Per cent
- Out of 100. The sign is %.
- Whole
- The full amount. The whole is always 100%.
Worked example
e.g. Find 25% of 80.
- 25% means 25 out of 100. That is the same as one quarter.
- One quarter means split into 4 equal parts.
- .
- So 25% of 80 is 20.
Learn these three and most questions get easy: 50% is a half, 25% is a quarter, 10% is divide by 10.
Practice
The pictures fade as you go. By the last few you are on your own.
1What percentage is shaded?with a picture
Answer50%. Half of 100 is 50.
2What percentage is shaded?with a picture
Answer10%. Ten squares out of 100.
3Find 50% of 60.with a hint
Need a hint?
50% is a half. What is half of 60?
Answer30.
4Find 10% of 250.with a hint
Need a hint?
10% means divide by 10.
Answer25.
5Find 25% of 40.on your own
Answer10.
6Find 10% of 90.on your own
Answer9.
7A shirt costs . It is 50% off. What do you pay?on your own
Answer. Half of 40 is 20.
8Find 75% of 80.on your own
Answer60. 75% is three quarters. One quarter of 80 is 20, so three quarters is 60.
Think about it
1
Why is 50% the same as one half?
One good answer50 out of 100 is half of the squares. Both names describe the same amount.
2
How can knowing 10% help you find 20% or 30%?
One good answerFind 10% first, then double it for 20% or treble it for 30%. It is much easier than working them out from scratch.
3
Can a percentage be more than 100?
One good answerYes. 100% is the whole thing, so 200% is twice as much. You see this when something doubles in price.
Common mistakes
Thinking 25% is always 25.
It is 25 out of every 100. 25% of 80 is 20, not 25. The answer depends on the whole.
Mixing up 10% and a tenth of the digits.
10% of 250 is 25, not 2.5. Divide the whole amount by 10.
Forgetting the whole is always 100%.
If 30% is used, then 70% is left, because the two must add to 100.