Year 6: Using percentages to compare
Part of the Year 6 percentages chapter. Chapter overview · whole chapter on one page
Using percentages to compare
Percentages let us compare things that have different totals. A class of 20 and a class of 40 cannot be compared by counting, but their percentages can. The rule is simple: change each amount to a percentage first, then compare.
For money, the saving is worked out in pounds, so compare the pounds saved. Do not compare the percentages of different prices.
Key ideas
- To compare two amounts out of different totals, change both to percentages first.
- A percentage is out of 100, so bigger percentages are bigger shares.
- For a sale, find the saving in pounds with the percentage, then compare the savings.
- If two answers are the same, say so: “They are both £6.”
Key words. The part is the number we are interested in. The whole is the total. To write a part as a percentage of the whole, divide the part by the whole and then multiply by 100.
Method. Change each one to a percentage out of 100, then compare.
- Change 18 out of 25 to a percentage. 18/25 = 0.72, and 0.72 × 100 = 72.18/25 = 72%
- Change 15 out of 20 to a percentage. 15/20 = 0.75, and 0.75 × 100 = 75.15/20 = 75%
- Compare the two percentages. Both are out of 100, so the bigger number is the bigger share.72% < 75%
- Write the answer. 15 out of 20 is the bigger share (75% against 72%).
Check. 72% is less than 75%, so the second result is better. ✓
Watch out. Compare percentages, not the numbers on top. 18 is more than 15, but 15 out of 20 is the bigger share.
Key words. The part is the number we are interested in. The whole is the total. To write a part as a percentage of the whole, divide the part by the whole and then multiply by 100.
Method. Find the saving in pounds for each shop, then compare the savings.
- Find the saving at Shop A: 20% of £45. 1% of £45 is £0.45, so 20% is 20 lots of that.20% of 45 = 9
- Find the saving at Shop B. Shop B takes £8 off the price.Saving = 8
- Compare the savings. The bigger saving is the better offer.9 > 8
- Write the answer. Shop A saves more: £9 against £8.
Check. Shop A: £45 − £9 = £36. Shop B: £40 − £8 = £32. Shop A saves more, although the two jackets have different prices. ✓
Watch out. Find the saving in pounds, then compare. Do not compare 20% with £8.
Key words. The part is the number we are interested in. The whole is the total. To write a part as a percentage of the whole, divide the part by the whole and then multiply by 100.
Method. Change both results to percentages of the class, then compare.
- Change class 6A to a percentage. 12 out of 30 pupils.12/30 = 40%
- Change class 6B to a percentage. 15 out of 40 pupils. 15 ÷ 40 = 0.375.15/40 = 0.375 = 37.5%
- Compare. 40 is bigger than 37.5.40% > 37.5%
- Write the answer. Class 6A (40% against 37.5%).
Check. Class 6A has the bigger percentage, even though 6B has more pupils who chose football. ✓
Watch out. More pupils does not always mean a bigger percentage.
Watch out
Do not compare the top numbers. 15 is less than 18, but 15 out of 20 (75%) is a bigger share than 18 out of 25 (72%).
Exam tip
Exam tip. When a question asks which is better, write both percentages and then say which is bigger in words.
Exercise 6E Comparing with percentages
Non-calculatorKey words. The part is the number we are interested in. The whole is the total. To write a part as a percentage of the whole, divide the part by the whole and then multiply by 100.
Method. Change each to a percentage, then compare.
- Write 3/5 as a percentage. 3 out of 5 is 60%.3/5 = 60%
- Compare with 58%. 60% is more than 58%.60% > 58%
- Write the answer. 3/5
Check. 3/5 is 60%, and 60% is more than 58%. ✓
Watch out. Change the fraction to a percentage before you compare.
Key words. The part is the number we are interested in. The whole is the total. To write a part as a percentage of the whole, divide the part by the whole and then multiply by 100.
Method. Change both to percentages, then compare.
- Write 3/4 as a percentage. 3 quarters is 75%.3/4 = 75%
- Compare with 70%. 75% is more than 70%.75% > 70%
- Write the answer. 3/4
Check. 3/4 of a cake is more than 70% of a cake. ✓
Watch out. 3/4 and 70% both describe parts of a cake, so compare them as percentages.
Key words. The part is the number we are interested in. The whole is the total. To write a part as a percentage of the whole, divide the part by the whole and then multiply by 100.
Method. Change each one to a percentage out of 100, then compare.
- Change 18 out of 25 to a percentage. 18/25 = 0.72, and 0.72 × 100 = 72.18/25 = 72%
- Change 33 out of 40 to a percentage. 33 ÷ 40 = 0.825, and 0.825 × 100 = 82.5.33/40 = 82.5%
- Compare the two percentages. Both are out of 100, so the bigger number is the bigger share.72% < 82.5%
- Write the answer. Ben did better (82.5% against 72%).
Check. 82.5% is more than 72%, so Ben did better. ✓
Watch out. Compare percentages, not the numbers on top. 18 is more than 15, but 15 out of 20 is the bigger share.
Key words. The part is the number we are interested in. The whole is the total. To write a part as a percentage of the whole, divide the part by the whole and then multiply by 100.
Method. Find each amount as a percentage of 250 or 120, then compare the amounts.
- Find 20% of 250. 1% of 250 is 2.5, so 20% is 20 lots of 2.5.20% of 250 = 50
- Find 35% of 120. 1% of 120 is 1.2, so 35% is 35 lots of 1.2.35% of 120 = 42
- Compare. 50 is more than 42.50 > 42
- Write the answer. 20% of 250 (which is 50)
Check. 50 is more than 42, so 20% of 250 is the bigger amount. ✓
Watch out. Do not compare 20 with 35. Find both amounts first.
Key words. The part is the number we are interested in. The whole is the total. To write a part as a percentage of the whole, divide the part by the whole and then multiply by 100.
Method. Find the saving in pounds for each coat, then compare.
- Find the saving at Shop X: 25% of £60. 1% of £60 is £0.60, so 25% is 25 lots of that. Or divide by 4.60 ÷ 4 = 15
- Find the saving at Shop Y. Shop Y takes £14 off.Saving = 14
- Compare. The bigger saving is better.15 > 14
- Write the answer. Shop X
Check. Shop X saves £15 and Shop Y saves £14. ✓
Watch out. The coat prices are different, so compare the savings, not the percentages.
Key words. The part is the number we are interested in. The whole is the total. To write a part as a percentage of the whole, divide the part by the whole and then multiply by 100.
Method. Find each saving in pounds, then compare.
- Find the saving at Shop P: 30% of £20. Divide 20 by 100, then multiply by 30.30% of 20 = 6
- Find the saving at Shop Q: a quarter of £24. A quarter is 25%, so divide by 4.24 ÷ 4 = 6
- Compare. Both savings are the same.6 = 6
- Write the answer. They are the same: £6 each.
Check. Both shops take £6 off. ✓
Watch out. Equal savings are possible even with different percentages and prices.
Key words. The part is the number we are interested in. The whole is the total. To write a part as a percentage of the whole, divide the part by the whole and then multiply by 100.
Method. Change each year group to a percentage, then compare.
- Year 4: 24 out of 60. 24 ÷ 60 = 0.4, which is 40%.24/60 = 40%
- Year 5: 27 out of 75. 27 ÷ 75 = 0.36, which is 36%.27/75 = 36%
- Compare. 40% is more than 36%.40% > 36%
- Write the answer. Year 4 (40% against 36%).
Check. Year 4 has the bigger percentage, although Year 5 has more pupils who like cats. ✓
Watch out. Compare the percentages, not the numbers of pupils.
Key words. The part is the number we are interested in. The whole is the total. To write a part as a percentage of the whole, divide the part by the whole and then multiply by 100.
Method. Find how many European stamps each person has, then compare the numbers.
- Find 40% of Ella’s 150 stamps. 1% of 150 is 1.5, so 40% is 40 lots of 1.5.40% of 150 = 60
- Find 45% of Jack’s 120 stamps. 1% of 120 is 1.2, so 45% is 45 lots of 1.2.45% of 120 = 54
- Compare the numbers of stamps. Compare the amounts, because both are amounts of stamps.60 > 54
- Write the answer. Ella has more European stamps (60 against 54).
Check. Ella has 60 and Jack has 54. Jack’s percentage is bigger, but he has fewer stamps. ✓
Watch out. Here the question asks for an amount, so compare the amounts, not the percentages.
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 as an amount, then compare.
- Find 30% of 200. 1% of 200 is 2, so 30% is 30 lots of 2.30% of 200 = 60
- Find 25% of 250. 1% of 250 is 2.5, so 25% is 25 lots of 2.5.25% of 250 = 62.5
- Compare. 62.5 is more than 60.62.5 > 60
- Write the answer. No. 25% of 250 = 62.5, which is more than 60.
Check. The percentage is smaller, but the amount is bigger. ✓
Watch out. A smaller percentage of a bigger amount can be the bigger answer.
Key words. The part is the number we are interested in. The whole is the total. To write a part as a percentage of the whole, divide the part by the whole and then multiply by 100.
Method. Change the fraction to a percentage, then compare with 85%.
- Write 7/8 as a decimal. 7 ÷ 8 = 0.875.7/8 = 0.875
- Write 0.875 as a percentage. Multiply by 100.0.875 × 100 = 87.5
- Compare with 85%. 87.5% is more than 85%.87.5% > 85%
- Write the answer. Yes. 7/8 = 87.5%, which is more than 85%.
Check. Each eighth is 12.5%, so 7 eighths is 87.5%. ✓
Watch out. Eighths are not in tenths or quarters, so change them to a decimal first.
Key words. The part is the number we are interested in. The whole is the total. To write a part as a percentage of the whole, divide the part by the whole and then multiply by 100.
Method. Change each class to a percentage, then compare.
- Class of 40: 12 left-handed. 12 out of 40.12/40 = 30%
- Class of 25: 8 left-handed. 8 out of 25.8/25 = 32%
- Compare. 32% is more than 30%.32% > 30%
- Write the answer. The class of 25 (32% against 30%).
Check. The smaller class has the bigger percentage. ✓
Watch out. Look at the percentages, not at the size of the class.