Year 6: Percentages of measures
Part of the Year 6 percentages chapter. Chapter overview · whole chapter on one page
Percentages of measures
A percentage of a measure is a part of an amount, such as a length, a mass, a volume or a sum of money. Two methods always work.
- Build it from 10%. Find 10% (divide by 10), then add the parts you need: 5% is half of 10%, and 1% is a tenth of 10%.
- Use 1% first. Divide the amount by 100 to find 1%, then multiply by the percentage.
For 15% of 360: 10% is 36, and 5% is half of 36, which is 18. So 15% is 36 + 18 = 54.
Key ideas
- A percentage of a measure is the same as the percentage times the amount, divided by 100.
- 10% is one tenth. 5% is half of 10%. 1% is one hundredth.
- Make the units the same before you calculate: 1 kg = 1000 g, 1 m = 100 cm, 1 litre = 1000 ml.
- Check that your answer is sensible: 15% of 360 must be less than 360.
Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.
Method. Find 10% first, then add the 5% and 1% parts that make up 15%.
- Split 15% into 10%, 5% and 1% parts. Ten, five and one make the parts we can find easily.15% = 1 lot of 10% + 5%
- Find 10% of 360, then 1 lot. 10% is one tenth, so divide by 10.10% of 360 = 36; 1 × 36 = 36
- Find 5%. Half of 10% is 5%, so halve the 10% answer.5% of 360 = 36 ÷ 2 = 18
- Add the parts. Add the answers for each part to find the whole percentage.36 + 18 = 54
Check. Fraction check: 15/100 × 360 = 54. ✓
Watch out. Check the parts: 10% is a tenth, so divide by 10. 1% is divide by 100.
Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.
Method. Find 1% first by dividing by 100, then multiply by 35.
- Write the percentage as a fraction out of 100. Per cent means out of 100.35% = 35/100
- Find 1% of 40. Divide by 100, because 1% is one hundredth.40 ÷ 100 = 0.4
- Multiply by 35. 35% is 35 lots of 1%.0.4 × 35 = 14
- Write the answer. 14
Check. 14 is less than 40, because 35% is less than 100%. ✓
Watch out. Dividing by 100 gives 1%. Do not multiply by 35 before you divide.
Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.
Method. Find 1% first by dividing by 100, then multiply by 12.
- Write the percentage as a fraction out of 100. Per cent means out of 100.12% = 12/100
- Find 1% of 4.5. Divide by 100, because 1% is one hundredth.4.5 ÷ 100 = 0.045
- Multiply by 12. 12% is 12 lots of 1%.0.045 × 12 = 0.54
- Write the answer. 0.54
Check. 0.54 is less than 4.5, because 12% is less than 100%. ✓
Watch out. Dividing by 100 gives 1%. Do not multiply by 12 before you divide.
Watch out
Take care with the decimal point. 1% of £4.50 is 4.5 ÷ 100 = 0.045, and 12 lots of that make 0.54. Your answer must be in pounds and pence.
Exam tip
Exam tip. If you are not sure which method to use, find 10% and 1% first. Those two are always quick.
Exercise 6D Finding percentages of measures
Non-calculatorKey words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.
Method. Find 10% first, then add the 5% and 1% parts that make up 15%.
- Split 15% into 10%, 5% and 1% parts. Ten, five and one make the parts we can find easily.15% = 1 lot of 10% + 5%
- Find 10% of 80, then 1 lot. 10% is one tenth, so divide by 10.10% of 80 = 8; 1 × 8 = 8
- Find 5%. Half of 10% is 5%, so halve the 10% answer.5% of 80 = 8 ÷ 2 = 4
- Add the parts. Add the answers for each part to find the whole percentage.8 + 4 = 12
Check. Fraction check: 15/100 × 80 = 12. ✓
Watch out. Check the parts: 10% is a tenth, so divide by 10. 1% is divide by 100.
Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.
Method. Find 10% first, then add the 5% and 1% parts that make up 15%.
- Split 15% into 10%, 5% and 1% parts. Ten, five and one make the parts we can find easily.15% = 1 lot of 10% + 5%
- Find 10% of 200, then 1 lot. 10% is one tenth, so divide by 10.10% of 200 = 20; 1 × 20 = 20
- Find 5%. Half of 10% is 5%, so halve the 10% answer.5% of 200 = 20 ÷ 2 = 10
- Add the parts. Add the answers for each part to find the whole percentage.20 + 10 = 30
Check. Fraction check: 15/100 × 200 = 30. ✓
Watch out. Check the parts: 10% is a tenth, so divide by 10. 1% is divide by 100.
Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.
Method. Find 10% first, then add the 5% and 1% parts that make up 35%.
- Split 35% into 10%, 5% and 1% parts. Ten, five and one make the parts we can find easily.35% = 3 lots of 10% + 5%
- Find 10% of 60, then 3 lots. 10% is one tenth, so divide by 10.10% of 60 = 6; 3 × 6 = 18
- Find 5%. Half of 10% is 5%, so halve the 10% answer.5% of 60 = 6 ÷ 2 = 3
- Add the parts. Add the answers for each part to find the whole percentage.18 + 3 = 21
Check. Fraction check: 35/100 × 60 = 21. ✓
Watch out. Check the parts: 10% is a tenth, so divide by 10. 1% is divide by 100.
Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.
Method. Find 10% first, then add the 5% and 1% parts that make up 5%.
- Split 5% into 10%, 5% and 1% parts. Ten, five and one make the parts we can find easily.5% = 5%
- Find 5%. Half of 10% is 5%, so halve the 10% answer.5% of 260 = 26 ÷ 2 = 13
- Add the parts. Add the answers for each part to find the whole percentage.13 = 13
Check. Fraction check: 5/100 × 260 = 13. ✓
Watch out. Check the parts: 10% is a tenth, so divide by 10. 1% is divide by 100.
Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.
Method. Find 10% first, then add the 5% and 1% parts that make up 40%.
- Split 40% into 10%, 5% and 1% parts. Ten, five and one make the parts we can find easily.40% = 4 lots of 10%
- Find 10% of 90, then 4 lots. 10% is one tenth, so divide by 10.10% of 90 = 9; 4 × 9 = 36
- Add the parts. Add the answers for each part to find the whole percentage.36 = 36
Check. Fraction check: 40/100 × 90 = 36. ✓
Watch out. Check the parts: 10% is a tenth, so divide by 10. 1% is divide by 100.
Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.
Method. Find 10% first, then add the 5% and 1% parts that make up 60%.
- Split 60% into 10%, 5% and 1% parts. Ten, five and one make the parts we can find easily.60% = 6 lots of 10%
- Find 10% of 45, then 6 lots. 10% is one tenth, so divide by 10.10% of 45 = 4.5; 6 × 4.5 = 27
- Add the parts. Add the answers for each part to find the whole percentage.27 = 27
Check. Fraction check: 60/100 × 45 = 27. ✓
Watch out. Check the parts: 10% is a tenth, so divide by 10. 1% is divide by 100.
Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.
Method. Find 10% first, then add the 5% and 1% parts that make up 8%.
- Split 8% into 10%, 5% and 1% parts. Ten, five and one make the parts we can find easily.8% = 5% + 3 lots of 1%
- Find 5%. Half of 10% is 5%, so halve the 10% answer.5% of 150 = 15 ÷ 2 = 7.5
- Find 1% of 150, then 3 lots. Divide by 100 for 1%.1% of 150 = 1.5; 3 × 1.5 = 4.5
- Add the parts. Add the answers for each part to find the whole percentage.7.5 + 4.5 = 12
Check. Fraction check: 8/100 × 150 = 12. ✓
Watch out. Check the parts: 10% is a tenth, so divide by 10. 1% is divide by 100.
Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.
Method. Find 10% first, then add the 5% and 1% parts that make up 17%.
- Split 17% into 10%, 5% and 1% parts. Ten, five and one make the parts we can find easily.17% = 1 lot of 10% + 5% + 2 lots of 1%
- Find 10% of 300, then 1 lot. 10% is one tenth, so divide by 10.10% of 300 = 30; 1 × 30 = 30
- Find 5%. Half of 10% is 5%, so halve the 10% answer.5% of 300 = 30 ÷ 2 = 15
- Find 1% of 300, then 2 lots. Divide by 100 for 1%.1% of 300 = 3; 2 × 3 = 6
- Add the parts. Add the answers for each part to find the whole percentage.30 + 15 + 6 = 51
Check. Fraction check: 17/100 × 300 = 51. ✓
Watch out. Check the parts: 10% is a tenth, so divide by 10. 1% is divide by 100.
Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.
Method. Find 10% first, then add the 5% and 1% parts that make up 2%.
- Split 2% into 10%, 5% and 1% parts. Ten, five and one make the parts we can find easily.2% = 2 lots of 1%
- Find 1% of 50, then 2 lots. Divide by 100 for 1%.1% of 50 = 0.5; 2 × 0.5 = 1
- Add the parts. Add the answers for each part to find the whole percentage.1 = 1
Check. Fraction check: 2/100 × 50 = 1. ✓
Watch out. Check the parts: 10% is a tenth, so divide by 10. 1% is divide by 100.
Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.
Method. Find 10% first, then add the 5% and 1% parts that make up 9%.
- Split 9% into 10%, 5% and 1% parts. Ten, five and one make the parts we can find easily.9% = 5% + 4 lots of 1%
- Find 5%. Half of 10% is 5%, so halve the 10% answer.5% of 200 = 20 ÷ 2 = 10
- Find 1% of 200, then 4 lots. Divide by 100 for 1%.1% of 200 = 2; 4 × 2 = 8
- Add the parts. Add the answers for each part to find the whole percentage.10 + 8 = 18
Check. Fraction check: 9/100 × 200 = 18. ✓
Watch out. Check the parts: 10% is a tenth, so divide by 10. 1% is divide by 100.
Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.
Method. Find 10% first, then add the 5% and 1% parts that make up 12%.
- Split 12% into 10%, 5% and 1% parts. Ten, five and one make the parts we can find easily.12% = 1 lot of 10% + 2 lots of 1%
- Find 10% of 50, then 1 lot. 10% is one tenth, so divide by 10.10% of 50 = 5; 1 × 5 = 5
- Find 1% of 50, then 2 lots. Divide by 100 for 1%.1% of 50 = 0.5; 2 × 0.5 = 1
- Add the parts. Add the answers for each part to find the whole percentage.5 + 1 = 6
Check. Fraction check: 12/100 × 50 = 6. ✓
Watch out. Check the parts: 10% is a tenth, so divide by 10. 1% is divide by 100.
Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.
Method. Find 10% first, then add the 5% and 1% parts that make up 30%.
- Split 30% into 10%, 5% and 1% parts. Ten, five and one make the parts we can find easily.30% = 3 lots of 10%
- Find 10% of 70, then 3 lots. 10% is one tenth, so divide by 10.10% of 70 = 7; 3 × 7 = 21
- Add the parts. Add the answers for each part to find the whole percentage.21 = 21
Check. Fraction check: 30/100 × 70 = 21. ✓
Watch out. Check the parts: 10% is a tenth, so divide by 10. 1% is divide by 100.
Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.
Method. Find 10% first, then add the 5% and 1% parts that make up 65%.
- Split 65% into 10%, 5% and 1% parts. Ten, five and one make the parts we can find easily.65% = 6 lots of 10% + 5%
- Find 10% of 20, then 6 lots. 10% is one tenth, so divide by 10.10% of 20 = 2; 6 × 2 = 12
- Find 5%. Half of 10% is 5%, so halve the 10% answer.5% of 20 = 2 ÷ 2 = 1
- Add the parts. Add the answers for each part to find the whole percentage.12 + 1 = 13
Check. Fraction check: 65/100 × 20 = 13. ✓
Watch out. Check the parts: 10% is a tenth, so divide by 10. 1% is divide by 100.
Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.
Method. Find 10% first, then add the 5% and 1% parts that make up 90%.
- Split 90% into 10%, 5% and 1% parts. Ten, five and one make the parts we can find easily.90% = 9 lots of 10%
- Find 10% of 30, then 9 lots. 10% is one tenth, so divide by 10.10% of 30 = 3; 9 × 3 = 27
- Add the parts. Add the answers for each part to find the whole percentage.27 = 27
Check. Fraction check: 90/100 × 30 = 27. ✓
Watch out. Check the parts: 10% is a tenth, so divide by 10. 1% is divide by 100.
Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.
Method. Find 1% first by dividing by 100, then multiply by 35.
- Write the percentage as a fraction out of 100. Per cent means out of 100.35% = 35/100
- Find 1% of 240. Divide by 100, because 1% is one hundredth.240 ÷ 100 = 2.4
- Multiply by 35. 35% is 35 lots of 1%.2.4 × 35 = 84
- Write the answer. 84
Check. 84 is less than 240, because 35% is less than 100%. ✓
Watch out. Dividing by 100 gives 1%. Do not multiply by 35 before you divide.
Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.
Method. Find 1% first by dividing by 100, then multiply by 15.
- Write the percentage as a fraction out of 100. Per cent means out of 100.15% = 15/100
- Find 1% of 2000. Divide by 100, because 1% is one hundredth.2000 ÷ 100 = 20
- Multiply by 15. 15% is 15 lots of 1%.20 × 15 = 300
- Write the answer. 300
Check. 300 is less than 2000, because 15% is less than 100%. ✓
Watch out. Dividing by 100 gives 1%. Do not multiply by 15 before you divide.
Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.
Method. Find 1% first by dividing by 100, then multiply by 40.
- Write the percentage as a fraction out of 100. Per cent means out of 100.40% = 40/100
- Find 1% of 3.5. Divide by 100, because 1% is one hundredth.3.5 ÷ 100 = 0.035
- Multiply by 40. 40% is 40 lots of 1%.0.035 × 40 = 1.4
- Write the answer. 1.4
Check. 1.4 is less than 3.5, because 40% is less than 100%. ✓
Watch out. Dividing by 100 gives 1%. Do not multiply by 40 before you divide.
Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.
Method. Find 1% first by dividing by 100, then multiply by 15.
- Write the percentage as a fraction out of 100. Per cent means out of 100.15% = 15/100
- Find 1% of 6.4. Divide by 100, because 1% is one hundredth.6.4 ÷ 100 = 0.064
- Multiply by 15. 15% is 15 lots of 1%.0.064 × 15 = 0.96
- Write the answer. 0.96
Check. 0.96 is less than 6.4, because 15% is less than 100%. ✓
Watch out. Dividing by 100 gives 1%. Do not multiply by 15 before you divide.
Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.
Method. Find 1% first by dividing by 100, then multiply by 35.
- Write the percentage as a fraction out of 100. Per cent means out of 100.35% = 35/100
- Find 1% of 80. Divide by 100, because 1% is one hundredth.80 ÷ 100 = 0.8
- Multiply by 35. 35% is 35 lots of 1%.0.8 × 35 = 28
- Write the answer. 28
Check. 28 is less than 80, because 35% is less than 100%. ✓
Watch out. Dividing by 100 gives 1%. Do not multiply by 35 before you divide.
Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.
Method. Find 10% first, then add the 5% and 1% parts that make up 20%.
- Split 20% into 10%, 5% and 1% parts. Ten, five and one make the parts we can find easily.20% = 2 lots of 10%
- Find 10% of 300, then 2 lots. 10% is one tenth, so divide by 10.10% of 300 = 30; 2 × 30 = 60
- Add the parts. Add the answers for each part to find the whole percentage.60 = 60
Check. Fraction check: 20/100 × 300 = 60. ✓
Watch out. Check the parts: 10% is a tenth, so divide by 10. 1% is divide by 100.
Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.
Method. Find 1% first by dividing by 100, then multiply by 6.
- Write the percentage as a fraction out of 100. Per cent means out of 100.6% = 6/100
- Find 1% of 2.5. Divide by 100, because 1% is one hundredth.2.5 ÷ 100 = 0.025
- Multiply by 6. 6% is 6 lots of 1%.0.025 × 6 = 0.15
- Write the answer. 0.15
Check. 0.15 is less than 2.5, because 6% is less than 100%. ✓
Watch out. Dividing by 100 gives 1%. Do not multiply by 6 before you divide.
Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.
Method. Work out each person’s answer, then decide.
- Ali: find 15% of 200. 10% is 20 and 5% is half of 20, which is 10.20 + 10 = 30, so 15% of 200 = 30
- Bea: find 20% of 150. 10% is 15, so 20% is two lots of 15.15 + 15 = 30, so 20% of 150 = 30
- Compare. Both answers are 30.30 = 30
- Write the answer. Both are right.
Check. Both people found 30. ✓
Watch out. Two different calculations can give the same answer.
Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.
Method. Work out each side, then compare.
- Find 25% of 80. One quarter of 80 is 80 ÷ 4.80 ÷ 4 = 20
- Find 80% of 25. 80% is 80 lots of 1%. 1% of 25 is 0.25, so 80 lots is 80 × 0.25.80 × 0.25 = 20
- Compare. The two answers are the same.20 = 20
- Write the answer. No. They are both 20, so Ben is not right.
Check. Ben thought 25% of 80 was more than 80% of 25. Both are 20. ✓
Watch out. A percentage of a number and the same percentage of the other way round are equal.