Year 6: Finding the numbers in a pie chart
Part of the Year 6 pie charts, line graphs and the mean chapter. Chapter overview · whole chapter on one page
Finding the numbers in a pie chart
Sometimes a pie chart stands for a total number, such as 120 pupils. Then each sector shows a number of pupils, and you can find that number from the sector.
There are two ways to do it. If the chart gives the angle, write the angle as a fraction of 360, then take that fraction of the total. If the chart gives a per cent, write the per cent as a fraction of 100, then take that fraction of the total.
Check your answer by adding all the sector numbers. They must add up to the total.
Key ideas
- Angle method: the number = angle ÷ 360 × total.
- Per cent method: the number = per cent ÷ 100 × total.
- The numbers in all the sectors add up to the total.
- A sector number is not the same as its angle. 135 degrees does not mean 135 pupils.
Key words. A pie chart shows a whole split into sectors. Each sector is a slice of the circle. The whole pie is 360 degrees, and it is also 100 per cent.
Method. Turn the angle into a fraction of the whole pie, then find that fraction of the total.
- Write the sector as a fraction of the whole pie. The whole pie is 360 degrees, so divide the angle by 360.135 ÷ 360 = 3/8
- Take that fraction of the total. The total is 120, so take the same fraction of it.3/8 × 120 = 45
- Write the answer. Apples has this many.45
Check. 45 out of 120 is the same fraction as 135 degrees out of 360. ✓
Watch out. Divide the angle by 360 first. Do not multiply the angle by the total.
Key words. A pie chart shows a whole split into sectors. Each sector is a slice of the circle. The whole pie is 360 degrees, and it is also 100 per cent.
Method. Change the per cent into a fraction, then take that fraction of the total.
- Write the per cent as a fraction. Per cent means out of 100.25/100 = 1/4
- Take that fraction of the total. The total is 40, so take 1/4 of it.1/4 × 40 = 10
- Write the answer. Cats has this many.10
Check. 10 is 1/4 of 40, so 25 per cent of 40 is 10. ✓
Watch out. Per cent is out of 100, not out of the total. Change it to a fraction first.
Key words. A pie chart shows a whole split into sectors. Each sector is a slice of the circle. The whole pie is 360 degrees, and it is also 100 per cent.
Method. Turn the angle into a fraction of the whole pie, then find that fraction of the total.
- Write the sector as a fraction of the whole pie. The whole pie is 360 degrees, so divide the angle by 360.80 ÷ 360 = 2/9
- Take that fraction of the total. The total is 90, so take the same fraction of it.2/9 × 90 = 20
- Write the answer. The sector has this many.20
Check. 20 out of 90 is the same fraction as 80 degrees out of 360. ✓
Watch out. Divide the angle by 360 first. Do not multiply the angle by the total.
Watch out
Common mistake: taking the angle as the number of children. A sector of 135 degrees is a little more than a third of the pie, so it is a little more than a third of the total. Always divide the angle by 360 first.
Exercise 12B Practice: finding the numbers in each sector
Non-calculatorKey words. A pie chart shows a whole split into sectors. Each sector is a slice of the circle. The whole pie is 360 degrees, and it is also 100 per cent.
Method. Turn the angle into a fraction of the whole pie, then find that fraction of the total.
- Write the sector as a fraction of the whole pie. The whole pie is 360 degrees, so divide the angle by 360.135 ÷ 360 = 3/8
- Take that fraction of the total. The total is 120, so take the same fraction of it.3/8 × 120 = 45
- Write the answer. Apples has this many.45
Check. 45 out of 120 is the same fraction as 135 degrees out of 360. ✓
Watch out. Divide the angle by 360 first. Do not multiply the angle by the total.
Key words. A pie chart shows a whole split into sectors. Each sector is a slice of the circle. The whole pie is 360 degrees, and it is also 100 per cent.
Method. Turn the angle into a fraction of the whole pie, then find that fraction of the total.
- Write the sector as a fraction of the whole pie. The whole pie is 360 degrees, so divide the angle by 360.63 ÷ 360 = 7/40
- Take that fraction of the total. The total is 120, so take the same fraction of it.7/40 × 120 = 21
- Write the answer. Grapes has this many.21
Check. 21 out of 120 is the same fraction as 63 degrees out of 360. ✓
Watch out. Divide the angle by 360 first. Do not multiply the angle by the total.
Key words. A pie chart shows a whole split into sectors. Each sector is a slice of the circle. The whole pie is 360 degrees, and it is also 100 per cent.
Method. Turn the angle into a fraction of the whole pie, then find that fraction of the total.
- Write the sector as a fraction of the whole pie. The whole pie is 360 degrees, so divide the angle by 360.90 ÷ 360 = 1/4
- Take that fraction of the total. The total is 120, so take the same fraction of it.1/4 × 120 = 30
- Write the answer. Bananas has this many.30
Check. 30 out of 120 is the same fraction as 90 degrees out of 360. ✓
Watch out. Divide the angle by 360 first. Do not multiply the angle by the total.
Key words. A pie chart shows a whole split into sectors. Each sector is a slice of the circle. The whole pie is 360 degrees, and it is also 100 per cent.
Method. Change the per cent into a fraction, then take that fraction of the total.
- Write the per cent as a fraction. Per cent means out of 100.25/100 = 1/4
- Take that fraction of the total. The total is 40, so take 1/4 of it.1/4 × 40 = 10
- Write the answer. Cats has this many.10
Check. 10 is 1/4 of 40, so 25 per cent of 40 is 10. ✓
Watch out. Per cent is out of 100, not out of the total. Change it to a fraction first.
Key words. A pie chart shows a whole split into sectors. Each sector is a slice of the circle. The whole pie is 360 degrees, and it is also 100 per cent.
Method. Change the per cent into a fraction, then take that fraction of the total.
- Write the per cent as a fraction. Per cent means out of 100.20/100 = 1/5
- Take that fraction of the total. The total is 40, so take 1/5 of it.1/5 × 40 = 8
- Write the answer. Fish has this many.8
Check. 8 is 1/5 of 40, so 20 per cent of 40 is 8. ✓
Watch out. Per cent is out of 100, not out of the total. Change it to a fraction first.
Key words. A pie chart shows a whole split into sectors. Each sector is a slice of the circle. The whole pie is 360 degrees, and it is also 100 per cent.
Method. Change the per cent into a fraction, then take that fraction of the total.
- Write the per cent as a fraction. Per cent means out of 100.35/100 = 7/20
- Take that fraction of the total. The total is 40, so take 7/20 of it.7/20 × 40 = 14
- Write the answer. Dogs has this many.14
Check. 14 is 7/20 of 40, so 35 per cent of 40 is 14. ✓
Watch out. Per cent is out of 100, not out of the total. Change it to a fraction first.
Key words. A pie chart shows a whole split into sectors. Each sector is a slice of the circle. The whole pie is 360 degrees, and it is also 100 per cent.
Method. Change the per cent into a fraction, then take that fraction of the total.
- Write the per cent as a fraction. Per cent means out of 100.10/100 = 1/10
- Take that fraction of the total. The total is 40, so take 1/10 of it.1/10 × 40 = 4
- Write the answer. None has this many.4
Check. 4 is 1/10 of 40, so 10 per cent of 40 is 4. ✓
Watch out. Per cent is out of 100, not out of the total. Change it to a fraction first.
Key words. A pie chart shows a whole split into sectors. Each sector is a slice of the circle. The whole pie is 360 degrees, and it is also 100 per cent.
Method. Turn the angle into a fraction of the whole pie, then find that fraction of the total.
- Write the sector as a fraction of the whole pie. The whole pie is 360 degrees, so divide the angle by 360.60 ÷ 360 = 1/6
- Take that fraction of the total. The total is 60, so take the same fraction of it.1/6 × 60 = 10
- Write the answer. Car has this many.10
Check. 10 out of 60 is the same fraction as 60 degrees out of 360. ✓
Watch out. Divide the angle by 360 first. Do not multiply the angle by the total.
Key words. A pie chart shows a whole split into sectors. Each sector is a slice of the circle. The whole pie is 360 degrees, and it is also 100 per cent.
Method. Turn the angle into a fraction of the whole pie, then find that fraction of the total.
- Write the sector as a fraction of the whole pie. The whole pie is 360 degrees, so divide the angle by 360.180 ÷ 360 = 1/2
- Take that fraction of the total. The total is 60, so take the same fraction of it.1/2 × 60 = 30
- Write the answer. Bus has this many.30
Check. 30 out of 60 is the same fraction as 180 degrees out of 360. ✓
Watch out. Divide the angle by 360 first. Do not multiply the angle by the total.
Key words. A pie chart shows a whole split into sectors. Each sector is a slice of the circle. The whole pie is 360 degrees, and it is also 100 per cent.
Method. Turn the angle into a fraction of the whole pie, then find that fraction of the total.
- Write the sector as a fraction of the whole pie. The whole pie is 360 degrees, so divide the angle by 360.48 ÷ 360 = 2/15
- Take that fraction of the total. The total is 60, so take the same fraction of it.2/15 × 60 = 8
- Write the answer. Bike has this many.8
Check. 8 out of 60 is the same fraction as 48 degrees out of 360. ✓
Watch out. Divide the angle by 360 first. Do not multiply the angle by the total.
Key words. A pie chart shows a whole split into sectors. Each sector is a slice of the circle. The whole pie is 360 degrees, and it is also 100 per cent.
Method. Take the bus pupils away from the total.
- Find the number of bus pupils. The bus sector is 180 degrees, which is half the pie.30 bus pupils
- Take them away from the total. The pupils who did not go by bus are all the others.60 − 30 = 30
- Write the answer. 30
Check. 30 + 30 = 60. ✓
Watch out. The bus sector is half the pie, so half the pupils went by bus.
Key words. A pie chart shows a whole split into sectors. Each sector is a slice of the circle. The whole pie is 360 degrees, and it is also 100 per cent.
Method. Turn the per cent into a fraction, then take that fraction of 40.
- Write 25 per cent as a fraction. Per cent means out of 100, and 25 out of 100 is a quarter.25/100 = 1/4
- Take a quarter of 40. Divide 40 by 4.40 ÷ 4 = 10
- Compare with Ruby. Ruby took 25 away from 40, which gives 15. That is not 25 per cent.40 − 25 = 15, which is wrong
Check. 10 is a quarter of 40, and 10 + 10 + 10 + 10 = 40. ✓
Watch out. Per cent is a fraction of the total, so multiply or divide. Subtracting from the total is a different question.
Key words. A pie chart shows a whole split into sectors. Each sector is a slice of the circle. The whole pie is 360 degrees, and it is also 100 per cent.
Method. Turn the angle into a fraction of the whole pie, then find that fraction of the total.
- Write the sector as a fraction of the whole pie. The whole pie is 360 degrees, so divide the angle by 360.150 ÷ 360 = 5/12
- Take that fraction of the total. The total is 60, so take the same fraction of it.5/12 × 60 = 25
- Write the answer. The sector has this many.25
Check. 25 out of 60 is the same fraction as 150 degrees out of 360. ✓
Watch out. Divide the angle by 360 first. Do not multiply the angle by the total.
Watch out
Watch out: check that the sector numbers add up to the total. If they do not, one of your answers is wrong.
Exam tip
Work with the fraction first, then multiply by the total. It is easier to check each step this way.