GCSE Maths: One quantity as a percentage of another (Higher)
Part of the GCSE Maths percentages chapter (Higher). Chapter overview · Foundation version of this lesson · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
One quantity as a percentage of another
Suppose 18 of the 25 students in a class walk to school. What percentage walk? You are being asked to write “18 out of 25” as a number out of 100. This is the reverse of the last section: instead of finding the part, you already know the part and the whole, and you want the percentage.
The method has two steps. Step 1: write the part over the whole as a fraction, partwhole. Step 2: change that fraction to a percentage. If the denominator goes into 100, make an equivalent fraction with denominator 100 (1825 = 72100 = 72%). If it does not, divide the top by the bottom and multiply by 100 (4260: 42 ÷ 60 = 0.7, and 0.7 × 100 = 70%). Both give the same kind of answer, and on a calculator the quick way is always part ÷ whole × 100.
Check the units first
The part and the whole must be measured in the same units before you divide. To write 45 minutes as a percentage of 2 hours, first change 2 hours to 120 minutes. Writing 452 would be a mistake because minutes and hours are different sizes.
Comparing using percentages
Which is the better test result: 18 out of 25, or 31 out of 40? The totals are different, so you cannot just compare 18 and 31. Percentages are all out of 100, so they put the results on the same scale. This is the main reason percentages are useful: they let you make a fair comparison.
The percentage can also be more than 100%. If you compare a new amount with an older, smaller one, the part is bigger than the whole you compare with. For example, 612 members this year compared with 480 last year: 612 ÷ 480 × 100 = 127.5%. That means there are 127.5% as many members as last year, so the club has grown.
Key ideas
- Percentage = part ÷ whole × 100.
- The part and the whole must be in the same units: change hours to minutes, pounds to pence, and so on.
- To compare two results with different totals, write both as percentages and compare those.
- A percentage can be bigger than 100% when the part is bigger than the amount it is compared with.
- Check: the percentage of the whole should give you back the part.
Method. To write one quantity as a percentage of another: write it as a fraction (part over whole), then change the fraction into a percentage.
- Write the part over the whole as a fraction. A percentage compares a part with the whole. Both numbers must be in the same units.4260
- Divide the top by the bottom. This changes the fraction into a decimal.42 ÷ 60 = 0.7
- Multiply by 100. To change a decimal into a percentage multiply by 100, because a percentage is a number out of 100.0.7 × 100 = 70%
Check. Check: 70% of 60 = 0.7 × 60 = 42, which is the part we started with. ✓
Watch out. Divide by the whole (the amount you are comparing with), not by the part.
Method. To write one quantity as a percentage of another: write it as a fraction (part over whole), then change the fraction into a percentage.
- Change both amounts to the same units. The part is in minutes and the whole is in hours. 1 hour = 60 minutes, so 2 hours = 120 minutes.2 hours = 2 × 60 = 120 minutes
- Write the part over the whole as a fraction. A percentage compares a part with the whole. Both numbers must be in the same units.45120
- Divide the top by the bottom. This changes the fraction into a decimal.45 ÷ 120 = 0.375
- Multiply by 100. To change a decimal into a percentage multiply by 100, because a percentage is a number out of 100.0.375 × 100 = 37.5%
Check. Check: 37.5% of 120 = 0.375 × 120 = 45, which is the part we started with. ✓
Watch out. Divide by the whole (the amount you are comparing with), not by the part.
Method. Percentages are all out of 100, so they let us compare amounts that have different totals.
- Write Zara as a percentage. To compare fairly we need the same total, so we use percentages (out of 100).1825 = 72100 = 72%
- Write Yusuf as a percentage. Do exactly the same for the second one.31 ÷ 40 = 0.775
0.775 × 100 = 77.5% - Compare the percentages. The bigger percentage is the better result.72% and 77.5%, so Yusuf is higher.
Check. Cross-check with decimals: 0.72 and 0.775; Yusuf is bigger. ✓
Watch out. Compare the percentages, not the raw scores. A bigger score can be a smaller percentage.
Method. To write one quantity as a percentage of another: write it as a fraction (part over whole), then change the fraction into a percentage.
- Write the part over the whole as a fraction. A percentage compares a part with the whole. Both numbers must be in the same units.612480
- Divide the top by the bottom. This changes the fraction into a decimal.612 ÷ 480 = 1.275
- Multiply by 100. To change a decimal into a percentage multiply by 100, because a percentage is a number out of 100.1.275 × 100 = 127.5%
Check. Check: 127.5% of 480 = 1.275 × 480 = 612, which is the part we started with. ✓
Watch out. Divide by the whole (the amount you are comparing with), not by the part.
Method. To write one quantity as a percentage of another: write it as a fraction (part over whole), then change the fraction into a percentage.
- Write the part over the whole as a fraction. A percentage compares a part with the whole. Both numbers must be in the same units.1128
- Divide the top by the bottom. This changes the fraction into a decimal.11 ÷ 28 = 0.392857…
- Multiply by 100. To change a decimal into a percentage multiply by 100, because a percentage is a number out of 100.0.392857… × 100 = 39.285714…%
- Round the answer. Round to 1 decimal place as the question asks.39.285714…% = 39.3% (to 1 d.p.)
Check. Check: 39.3% of 28 is about 11.00, which is very close to 11. ✓
Watch out. Divide by the whole (the amount you are comparing with), not by the part.
Method. Turn each percentage into a decimal multiplier, then multiply the two multipliers.
- Write A in terms of B. 40% as a decimal is 0.4. “A is 40% of B” means A = 0.4 × B.A = 0.4 × B
- Write B in terms of C. 25% as a decimal is 0.25.B = 0.25 × C
- Put the second line into the first. Replace B with 0.25 × C.A = 0.4 × 0.25 × C = 0.1 × C
- Change the multiplier into a percentage. Multiply by 100.0.1 = 10%
Check. Try C = 200: B is 25% of 200 = 50, and A is 40% of 50 = 20. Then 20 is 10% of 200. ✓
Watch out. Do not add 40% and 25%. The second percentage is of a different amount.
Watch out
Divide by the whole, the amount you are comparing with — and keep the units the same. “45 minutes out of 2 hours” is 45 out of 120, not 45 out of 2. Also, 18 out of 25 and 25 out of 18 are different: the order matters.Exercise 5D One quantity as a percentage of another (non-calculator)
Non-calculatorMethod. To write one quantity as a percentage of another: write it as a fraction (part over whole), then change the fraction into a percentage.
- Write the part over the whole as a fraction. A percentage compares a part with the whole. Both numbers must be in the same units.920
- Make the denominator 100. “Per cent” means out of 100. Multiply the top and the bottom by the same number: 20 × 5 = 100.920 = 45100 = 45%
Check. Check: 45% of 20 = 0.45 × 20 = 9, which is the part we started with. ✓
Watch out. Divide by the whole (the amount you are comparing with), not by the part.
Method. To write one quantity as a percentage of another: write it as a fraction (part over whole), then change the fraction into a percentage.
- Write the part over the whole as a fraction. A percentage compares a part with the whole. Both numbers must be in the same units.1250
- Make the denominator 100. “Per cent” means out of 100. Multiply the top and the bottom by the same number: 50 × 2 = 100.1250 = 24100 = 24%
Check. Check: 24% of 50 = 0.24 × 50 = 12, which is the part we started with. ✓
Watch out. Divide by the whole (the amount you are comparing with), not by the part.
Method. To write one quantity as a percentage of another: write it as a fraction (part over whole), then change the fraction into a percentage.
- Write the part over the whole as a fraction. A percentage compares a part with the whole. Both numbers must be in the same units.1825
- Make the denominator 100. “Per cent” means out of 100. Multiply the top and the bottom by the same number: 25 × 4 = 100.1825 = 72100 = 72%
Check. Check: 72% of 25 = 0.72 × 25 = 18, which is the part we started with. ✓
Watch out. Divide by the whole (the amount you are comparing with), not by the part.
Method. To write one quantity as a percentage of another: write it as a fraction (part over whole), then change the fraction into a percentage.
- Write the part over the whole as a fraction. A percentage compares a part with the whole. Both numbers must be in the same units.34
- Make the denominator 100. “Per cent” means out of 100. Multiply the top and the bottom by the same number: 4 × 25 = 100.34 = 75100 = 75%
Check. Check: 75% of 4 = 0.75 × 4 = 3, which is the part we started with. ✓
Watch out. Divide by the whole (the amount you are comparing with), not by the part.
Method. To write one quantity as a percentage of another: write it as a fraction (part over whole), then change the fraction into a percentage.
- Write the part over the whole as a fraction. A percentage compares a part with the whole. Both numbers must be in the same units.30200
- Divide the top by the bottom. This changes the fraction into a decimal.30 ÷ 200 = 0.15
- Multiply by 100. To change a decimal into a percentage multiply by 100, because a percentage is a number out of 100.0.15 × 100 = 15%
Check. Check: 15% of 200 = 0.15 × 200 = 30, which is the part we started with. ✓
Watch out. Divide by the whole (the amount you are comparing with), not by the part.
Method. To write one quantity as a percentage of another: write it as a fraction (part over whole), then change the fraction into a percentage.
- Write the part over the whole as a fraction. A percentage compares a part with the whole. Both numbers must be in the same units.710
- Make the denominator 100. “Per cent” means out of 100. Multiply the top and the bottom by the same number: 10 × 10 = 100.710 = 70100 = 70%
Check. Check: 70% of 10 = 0.7 × 10 = 7, which is the part we started with. ✓
Watch out. Divide by the whole (the amount you are comparing with), not by the part.
Method. To write one quantity as a percentage of another: write it as a fraction (part over whole), then change the fraction into a percentage.
- Write the part over the whole as a fraction. A percentage compares a part with the whole. Both numbers must be in the same units.2160
- Divide the top by the bottom. This changes the fraction into a decimal.21 ÷ 60 = 0.35
- Multiply by 100. To change a decimal into a percentage multiply by 100, because a percentage is a number out of 100.0.35 × 100 = 35%
Check. Check: 35% of 60 = 0.35 × 60 = 21, which is the part we started with. ✓
Watch out. Divide by the whole (the amount you are comparing with), not by the part.
Method. To write one quantity as a percentage of another: write it as a fraction (part over whole), then change the fraction into a percentage.
- Write the part over the whole as a fraction. A percentage compares a part with the whole. Both numbers must be in the same units.45120
- Divide the top by the bottom. This changes the fraction into a decimal.45 ÷ 120 = 0.375
- Multiply by 100. To change a decimal into a percentage multiply by 100, because a percentage is a number out of 100.0.375 × 100 = 37.5%
Check. Check: 37.5% of 120 = 0.375 × 120 = 45, which is the part we started with. ✓
Watch out. Divide by the whole (the amount you are comparing with), not by the part.
Method. To write one quantity as a percentage of another: write it as a fraction (part over whole), then change the fraction into a percentage.
- Write the part over the whole as a fraction. A percentage compares a part with the whole. Both numbers must be in the same units.940
- Divide the top by the bottom. This changes the fraction into a decimal.9 ÷ 40 = 0.225
- Multiply by 100. To change a decimal into a percentage multiply by 100, because a percentage is a number out of 100.0.225 × 100 = 22.5%
Check. Check: 22.5% of 40 = 0.225 × 40 = 9, which is the part we started with. ✓
Watch out. Divide by the whole (the amount you are comparing with), not by the part.
Method. To write one quantity as a percentage of another: write it as a fraction (part over whole), then change the fraction into a percentage.
- Write the part over the whole as a fraction. A percentage compares a part with the whole. Both numbers must be in the same units.66120
- Divide the top by the bottom. This changes the fraction into a decimal.66 ÷ 120 = 0.55
- Multiply by 100. To change a decimal into a percentage multiply by 100, because a percentage is a number out of 100.0.55 × 100 = 55%
Check. Check: 55% of 120 = 0.55 × 120 = 66, which is the part we started with. ✓
Watch out. Divide by the whole (the amount you are comparing with), not by the part.
Method. To write one quantity as a percentage of another: write it as a fraction (part over whole), then change the fraction into a percentage.
- Change both amounts to the same units. 1 m = 100 cm, so we change the metres to centimetres.2 m = 2 × 100 = 200 cm
- Write the part over the whole as a fraction. A percentage compares a part with the whole. Both numbers must be in the same units.30200
- Divide the top by the bottom. This changes the fraction into a decimal.30 ÷ 200 = 0.15
- Multiply by 100. To change a decimal into a percentage multiply by 100, because a percentage is a number out of 100.0.15 × 100 = 15%
Check. Check: 15% of 200 = 0.15 × 200 = 30, which is the part we started with. ✓
Watch out. Divide by the whole (the amount you are comparing with), not by the part.
Method. To write one quantity as a percentage of another: write it as a fraction (part over whole), then change the fraction into a percentage.
- Change both amounts to the same units. 1 hour = 60 minutes.3 hours = 3 × 60 = 180 minutes
- Write the part over the whole as a fraction. A percentage compares a part with the whole. Both numbers must be in the same units.45180
- Divide the top by the bottom. This changes the fraction into a decimal.45 ÷ 180 = 0.25
- Multiply by 100. To change a decimal into a percentage multiply by 100, because a percentage is a number out of 100.0.25 × 100 = 25%
Check. Check: 25% of 180 = 0.25 × 180 = 45, which is the part we started with. ✓
Watch out. Divide by the whole (the amount you are comparing with), not by the part.
Method. To write one quantity as a percentage of another: write it as a fraction (part over whole), then change the fraction into a percentage.
- Change both amounts to the same units. £1 = 100p.£2.40 = 2.40 × 100 = 240p
- Write the part over the whole as a fraction. A percentage compares a part with the whole. Both numbers must be in the same units.60240
- Divide the top by the bottom. This changes the fraction into a decimal.60 ÷ 240 = 0.25
- Multiply by 100. To change a decimal into a percentage multiply by 100, because a percentage is a number out of 100.0.25 × 100 = 25%
Check. Check: 25% of 240 = 0.25 × 240 = 60, which is the part we started with. ✓
Watch out. Divide by the whole (the amount you are comparing with), not by the part.
Method. To write one quantity as a percentage of another: write it as a fraction (part over whole), then change the fraction into a percentage.
- Change both amounts to the same units. 1 kg = 1,000 g.2 kg = 2 × 1,000 = 2,000 g
- Write the part over the whole as a fraction. A percentage compares a part with the whole. Both numbers must be in the same units.2502,000
- Divide the top by the bottom. This changes the fraction into a decimal.250 ÷ 2,000 = 0.125
- Multiply by 100. To change a decimal into a percentage multiply by 100, because a percentage is a number out of 100.0.125 × 100 = 12.5%
Check. Check: 12.5% of 2,000 = 0.125 × 2,000 = 250, which is the part we started with. ✓
Watch out. Divide by the whole (the amount you are comparing with), not by the part.
Method. To write one quantity as a percentage of another: write it as a fraction (part over whole), then change the fraction into a percentage.
- Change both amounts to the same units. 1 km = 1,000 m.2.4 km = 2.4 × 1,000 = 2,400 m
- Write the part over the whole as a fraction. A percentage compares a part with the whole. Both numbers must be in the same units.6002,400
- Divide the top by the bottom. This changes the fraction into a decimal.600 ÷ 2,400 = 0.25
- Multiply by 100. To change a decimal into a percentage multiply by 100, because a percentage is a number out of 100.0.25 × 100 = 25%
Check. Check: 25% of 2,400 = 0.25 × 2,400 = 600, which is the part we started with. ✓
Watch out. Divide by the whole (the amount you are comparing with), not by the part.
Method. To write one quantity as a percentage of another: write it as a fraction (part over whole), then change the fraction into a percentage.
- Change both amounts to the same units. 1 minute = 60 seconds.1 minute = 60 seconds
- Write the part over the whole as a fraction. A percentage compares a part with the whole. Both numbers must be in the same units.1560
- Divide the top by the bottom. This changes the fraction into a decimal.15 ÷ 60 = 0.25
- Multiply by 100. To change a decimal into a percentage multiply by 100, because a percentage is a number out of 100.0.25 × 100 = 25%
Check. Check: 25% of 60 = 0.25 × 60 = 15, which is the part we started with. ✓
Watch out. Divide by the whole (the amount you are comparing with), not by the part.
Method. To write one quantity as a percentage of another: write it as a fraction (part over whole), then change the fraction into a percentage.
- Write the part over the whole as a fraction. A percentage compares a part with the whole. Both numbers must be in the same units.1440
- Divide the top by the bottom. This changes the fraction into a decimal.14 ÷ 40 = 0.35
- Multiply by 100. To change a decimal into a percentage multiply by 100, because a percentage is a number out of 100.0.35 × 100 = 35%
Check. Check: 35% of 40 = 0.35 × 40 = 14, which is the part we started with. ✓
Watch out. Divide by the whole (the amount you are comparing with), not by the part.
Method. To write one quantity as a percentage of another: write it as a fraction (part over whole), then change the fraction into a percentage.
- Write the part over the whole as a fraction. A percentage compares a part with the whole. Both numbers must be in the same units.4001,000
- Divide the top by the bottom. This changes the fraction into a decimal.400 ÷ 1,000 = 0.4
- Multiply by 100. To change a decimal into a percentage multiply by 100, because a percentage is a number out of 100.0.4 × 100 = 40%
Check. Check: 40% of 1,000 = 0.4 × 1,000 = 400, which is the part we started with. ✓
Watch out. Divide by the whole (the amount you are comparing with), not by the part.
Method. To write one quantity as a percentage of another: write it as a fraction (part over whole), then change the fraction into a percentage.
- Write the part over the whole as a fraction. A percentage compares a part with the whole. Both numbers must be in the same units.2501,000
- Divide the top by the bottom. This changes the fraction into a decimal.250 ÷ 1,000 = 0.25
- Multiply by 100. To change a decimal into a percentage multiply by 100, because a percentage is a number out of 100.0.25 × 100 = 25%
Check. Check: 25% of 1,000 = 0.25 × 1,000 = 250, which is the part we started with. ✓
Watch out. Divide by the whole (the amount you are comparing with), not by the part.
Method. To write one quantity as a percentage of another: write it as a fraction (part over whole), then change the fraction into a percentage.
- Write the part over the whole as a fraction. A percentage compares a part with the whole. Both numbers must be in the same units.1501,000
- Divide the top by the bottom. This changes the fraction into a decimal.150 ÷ 1,000 = 0.15
- Multiply by 100. To change a decimal into a percentage multiply by 100, because a percentage is a number out of 100.0.15 × 100 = 15%
Check. Check: 15% of 1,000 = 0.15 × 1,000 = 150, which is the part we started with. ✓
Watch out. Divide by the whole (the amount you are comparing with), not by the part.
Method. To write one quantity as a percentage of another: write it as a fraction (part over whole), then change the fraction into a percentage.
- Write the part over the whole as a fraction. A percentage compares a part with the whole. Both numbers must be in the same units.1201,000
- Divide the top by the bottom. This changes the fraction into a decimal.120 ÷ 1,000 = 0.12
- Multiply by 100. To change a decimal into a percentage multiply by 100, because a percentage is a number out of 100.0.12 × 100 = 12%
Check. Check: 12% of 1,000 = 0.12 × 1,000 = 120, which is the part we started with. ✓
Watch out. Divide by the whole (the amount you are comparing with), not by the part.
Method. To write one quantity as a percentage of another: write it as a fraction (part over whole), then change the fraction into a percentage.
- Write the part over the whole as a fraction. A percentage compares a part with the whole. Both numbers must be in the same units.801,000
- Divide the top by the bottom. This changes the fraction into a decimal.80 ÷ 1,000 = 0.08
- Multiply by 100. To change a decimal into a percentage multiply by 100, because a percentage is a number out of 100.0.08 × 100 = 8%
Check. Check: 8% of 1,000 = 0.08 × 1,000 = 80, which is the part we started with. ✓
Watch out. Divide by the whole (the amount you are comparing with), not by the part.
Method. To write one quantity as a percentage of another: write it as a fraction (part over whole), then change the fraction into a percentage.
- Write the part over the whole as a fraction. A percentage compares a part with the whole. Both numbers must be in the same units.2432
- Divide the top by the bottom. This changes the fraction into a decimal.24 ÷ 32 = 0.75
- Multiply by 100. To change a decimal into a percentage multiply by 100, because a percentage is a number out of 100.0.75 × 100 = 75%
Check. Check: 75% of 32 = 0.75 × 32 = 24, which is the part we started with. ✓
Watch out. Divide by the whole (the amount you are comparing with), not by the part.
Method. Percentages are all out of 100, so they let us compare amounts that have different totals.
- Write maths as a percentage. To compare fairly we need the same total, so we use percentages (out of 100).3650 = 72100 = 72%
- Write science as a percentage. Do exactly the same for the second one.52 ÷ 80 = 0.65
0.65 × 100 = 65% - Compare the percentages. The bigger percentage is the better result.72% and 65%, so maths is higher.
Check. Cross-check with decimals: 0.72 and 0.65; maths is bigger. ✓
Watch out. Compare the percentages, not the raw scores. A bigger score can be a smaller percentage.
Method. Find the percentage properly, and then see what went wrong.
- Write the fraction out of 20. The whole is 20, not 100.820
- Make the denominator 100. Multiply the top and bottom by 5, because 20 × 5 = 100.820 = 40100 = 40%
- Explain the mistake. The top number only gives the percentage when the whole is 100. Here the whole is 20.Tom forgot to scale up to 100.
Check. 40% of 20 = 0.4 × 20 = 8. ✓
Watch out. Only when the whole is exactly 100 can you read the percentage straight from the top.
Method. Write both results as percentages and compare them.
- Shop A as a percentage. Part over whole, then scale to 100 (or divide).18 ÷ 24 = 0.75, and 0.75 × 100 = 75%
- Shop B as a percentage. Do the same.27 ÷ 36 = 0.75, and 0.75 × 100 = 75%
- Compare. The percentages are equal.Neither shop is better: both are 75%.
Check. 1824 = 34 and 2736 = 34, so the fractions are equal too. ✓
Watch out. A bigger number of satisfied customers does not mean a better shop: compare percentages.
Method. To write one quantity as a percentage of another: write it as a fraction (part over whole), then change the fraction into a percentage.
- Write the part over the whole as a fraction. A percentage compares a part with the whole. Both numbers must be in the same units.500400
- Divide the top by the bottom. This changes the fraction into a decimal.500 ÷ 400 = 1.25
- Multiply by 100. To change a decimal into a percentage multiply by 100, because a percentage is a number out of 100.1.25 × 100 = 125%
Check. Check: 125% of 400 = 1.25 × 400 = 500, which is the part we started with. ✓
Watch out. Divide by the whole (the amount you are comparing with), not by the part.
Method. Multiply the two decimal multipliers together.
- Write A in terms of B. 40% = 0.4.A = 0.4 × B
- Write B in terms of C. 25% = 0.25.B = 0.25 × C
- Combine. Replace B in the first line.A = 0.4 × 0.25 × C = 0.1 × C
- Write as a percentage. Multiply by 100.0.1 = 10%
Check. If C = 100, then B = 25 and A = 40% of 25 = 10, which is 10% of 100. ✓
Watch out. The 25% is of C, not of A: do not just add or subtract the percentages.
Method. Part over whole each time, then compare the two answers.
- Write 45 as a percentage of 36. The part is 45 and the whole is 36.45 ÷ 36 = 1.25, and 1.25 × 100 = 125%
- Write 36 as a percentage of 45. Now the part is 36 and the whole is 45.36 ÷ 45 = 0.8, and 0.8 × 100 = 80%
- Explain why they are different. The whole is different each time. We always divide by the amount we compare with.125% and 80% are not the same.
Check. 125% of 36 = 1.25 × 36 = 45, and 80% of 45 = 0.8 × 45 = 36. ✓
Watch out. Always divide by the amount that comes after the word “of”.
Exercise 5E One quantity as a percentage of another (calculator)
Calculator allowedMethod. To write one quantity as a percentage of another: write it as a fraction (part over whole), then change the fraction into a percentage.
- Write the part over the whole as a fraction. A percentage compares a part with the whole. Both numbers must be in the same units.1745
- Divide the top by the bottom. This changes the fraction into a decimal.17 ÷ 45 = 0.377778…
- Multiply by 100. To change a decimal into a percentage multiply by 100, because a percentage is a number out of 100.0.377778… × 100 = 37.777778…%
- Round the answer. Round to 1 decimal place as the question asks.37.777778…% = 37.8% (to 1 d.p.)
Check. Check: 37.8% of 45 is about 17.01, which is very close to 17. ✓
Watch out. Divide by the whole (the amount you are comparing with), not by the part.
Method. To write one quantity as a percentage of another: write it as a fraction (part over whole), then change the fraction into a percentage.
- Write the part over the whole as a fraction. A percentage compares a part with the whole. Both numbers must be in the same units.2336
- Divide the top by the bottom. This changes the fraction into a decimal.23 ÷ 36 = 0.638889…
- Multiply by 100. To change a decimal into a percentage multiply by 100, because a percentage is a number out of 100.0.638889… × 100 = 63.888889…%
- Round the answer. Round to 1 decimal place as the question asks.63.888889…% = 63.9% (to 1 d.p.)
Check. Check: 63.9% of 36 is about 23.00, which is very close to 23. ✓
Watch out. Divide by the whole (the amount you are comparing with), not by the part.
Method. To write one quantity as a percentage of another: write it as a fraction (part over whole), then change the fraction into a percentage.
- Write the part over the whole as a fraction. A percentage compares a part with the whole. Both numbers must be in the same units.57
- Divide the top by the bottom. This changes the fraction into a decimal.5 ÷ 7 = 0.714286…
- Multiply by 100. To change a decimal into a percentage multiply by 100, because a percentage is a number out of 100.0.714286… × 100 = 71.428571…%
- Round the answer. Round to 1 decimal place as the question asks.71.428571…% = 71.4% (to 1 d.p.)
Check. Check: 71.4% of 7 is about 5.00, which is very close to 5. ✓
Watch out. Divide by the whole (the amount you are comparing with), not by the part.
Method. To write one quantity as a percentage of another: write it as a fraction (part over whole), then change the fraction into a percentage.
- Write the part over the whole as a fraction. A percentage compares a part with the whole. Both numbers must be in the same units.129150
- Divide the top by the bottom. This changes the fraction into a decimal.129 ÷ 150 = 0.86
- Multiply by 100. To change a decimal into a percentage multiply by 100, because a percentage is a number out of 100.0.86 × 100 = 86%
Check. Check: 86% of 150 = 0.86 × 150 = 129, which is the part we started with. ✓
Watch out. Divide by the whole (the amount you are comparing with), not by the part.
Method. To write one quantity as a percentage of another: write it as a fraction (part over whole), then change the fraction into a percentage.
- Write the part over the whole as a fraction. A percentage compares a part with the whole. Both numbers must be in the same units.813
- Divide the top by the bottom. This changes the fraction into a decimal.8 ÷ 13 = 0.615385…
- Multiply by 100. To change a decimal into a percentage multiply by 100, because a percentage is a number out of 100.0.615385… × 100 = 61.538462…%
- Round the answer. Round to 1 decimal place as the question asks.61.538462…% = 61.5% (to 1 d.p.)
Check. Check: 61.5% of 13 is about 8.00, which is very close to 8. ✓
Watch out. Divide by the whole (the amount you are comparing with), not by the part.
Method. To write one quantity as a percentage of another: write it as a fraction (part over whole), then change the fraction into a percentage.
- Write the part over the whole as a fraction. A percentage compares a part with the whole. Both numbers must be in the same units.345420
- Divide the top by the bottom. This changes the fraction into a decimal.345 ÷ 420 = 0.821429…
- Multiply by 100. To change a decimal into a percentage multiply by 100, because a percentage is a number out of 100.0.821429… × 100 = 82.142857…%
- Round the answer. Round to 1 decimal place as the question asks.82.142857…% = 82.1% (to 1 d.p.)
Check. Check: 82.1% of 420 is about 344.82, which is very close to 345. ✓
Watch out. Divide by the whole (the amount you are comparing with), not by the part.
Method. To write one quantity as a percentage of another: write it as a fraction (part over whole), then change the fraction into a percentage.
- Write the part over the whole as a fraction. A percentage compares a part with the whole. Both numbers must be in the same units.91240
- Divide the top by the bottom. This changes the fraction into a decimal.91 ÷ 240 = 0.379167…
- Multiply by 100. To change a decimal into a percentage multiply by 100, because a percentage is a number out of 100.0.379167… × 100 = 37.916667…%
- Round the answer. Round to 1 decimal place as the question asks.37.916667…% = 37.9% (to 1 d.p.)
Check. Check: 37.9% of 240 is about 90.96, which is very close to 91. ✓
Watch out. Divide by the whole (the amount you are comparing with), not by the part.
Method. To write one quantity as a percentage of another: write it as a fraction (part over whole), then change the fraction into a percentage.
- Write the part over the whole as a fraction. A percentage compares a part with the whole. Both numbers must be in the same units.285750
- Divide the top by the bottom. This changes the fraction into a decimal.285 ÷ 750 = 0.38
- Multiply by 100. To change a decimal into a percentage multiply by 100, because a percentage is a number out of 100.0.38 × 100 = 38%
Check. Check: 38% of 750 = 0.38 × 750 = 285, which is the part we started with. ✓
Watch out. Divide by the whole (the amount you are comparing with), not by the part.
Method. To write one quantity as a percentage of another: write it as a fraction (part over whole), then change the fraction into a percentage.
- Write the part over the whole as a fraction. A percentage compares a part with the whole. Both numbers must be in the same units.52,31048,500
- Divide the top by the bottom. This changes the fraction into a decimal.52,310 ÷ 48,500 = 1.078557…
- Multiply by 100. To change a decimal into a percentage multiply by 100, because a percentage is a number out of 100.1.078557… × 100 = 107.855670…%
- Round the answer. Round to 1 decimal place as the question asks.107.855670…% = 107.9% (to 1 d.p.)
Check. Check: 107.9% of 48,500 is about 52,331.50, which is very close to 52,310. ✓
Watch out. Divide by the whole (the amount you are comparing with), not by the part.
Method. To write one quantity as a percentage of another: write it as a fraction (part over whole), then change the fraction into a percentage.
- Write the part over the whole as a fraction. A percentage compares a part with the whole. Both numbers must be in the same units.7.512
- Divide the top by the bottom. This changes the fraction into a decimal.7.5 ÷ 12 = 0.625
- Multiply by 100. To change a decimal into a percentage multiply by 100, because a percentage is a number out of 100.0.625 × 100 = 62.5%
Check. Check: 62.5% of 12 = 0.625 × 12 = 7.5, which is the part we started with. ✓
Watch out. Divide by the whole (the amount you are comparing with), not by the part.
Method. Percentages are all out of 100, so they let us compare amounts that have different totals.
- Write Amy as a percentage. To compare fairly we need the same total, so we use percentages (out of 100).68 ÷ 85 = 0.8
0.8 × 100 = 80% - Write Ben as a percentage. Do exactly the same for the second one.74 ÷ 95 = 0.778947…
0.778947… × 100 = 77.894737…%
77.894737…% = 77.9% (to 1 d.p.) - Compare the percentages. The bigger percentage is the better result.80% and 77.9%, so Amy is higher.
Check. Cross-check with decimals: 0.8 and 0.778947…; Amy is bigger. ✓
Watch out. Compare the percentages, not the raw scores. A bigger score can be a smaller percentage.
Method. Percentages are all out of 100, so they let us compare amounts that have different totals.
- Write Ella as a percentage. To compare fairly we need the same total, so we use percentages (out of 100).14 ÷ 22 = 0.636364…
0.636364… × 100 = 63.636364…%
63.636364…% = 63.6% (to 1 d.p.) - Write Fatima as a percentage. Do exactly the same for the second one.19 ÷ 30 = 0.633333…
0.633333… × 100 = 63.333333…%
63.333333…% = 63.3% (to 1 d.p.) - Compare the percentages. The bigger percentage is the better result.63.6% and 63.3%, so Ella is higher.
Check. Cross-check with decimals: 0.636364… and 0.633333…; Ella is bigger. ✓
Watch out. Compare the percentages, not the raw scores. A bigger score can be a smaller percentage.
Method. To write one quantity as a percentage of another: write it as a fraction (part over whole), then change the fraction into a percentage.
- Write the part over the whole as a fraction. A percentage compares a part with the whole. Both numbers must be in the same units.134200
- Divide the top by the bottom. This changes the fraction into a decimal.134 ÷ 200 = 0.67
- Multiply by 100. To change a decimal into a percentage multiply by 100, because a percentage is a number out of 100.0.67 × 100 = 67%
Check. Check: 67% of 200 = 0.67 × 200 = 134, which is the part we started with. ✓
Watch out. Divide by the whole (the amount you are comparing with), not by the part.
Method. To write one quantity as a percentage of another: write it as a fraction (part over whole), then change the fraction into a percentage.
- Write the part over the whole as a fraction. A percentage compares a part with the whole. Both numbers must be in the same units.84,0001,200,000
- Divide the top by the bottom. This changes the fraction into a decimal.84,000 ÷ 1,200,000 = 0.07
- Multiply by 100. To change a decimal into a percentage multiply by 100, because a percentage is a number out of 100.0.07 × 100 = 7%
Check. Check: 7% of 1,200,000 = 0.07 × 1,200,000 = 84,000, which is the part we started with. ✓
Watch out. Divide by the whole (the amount you are comparing with), not by the part.
| Class | Passed | Students |
|---|---|---|
| A | 13 | 20 |
| B | 20 | 32 |
| C | 17 | 25 |
Method. Write each pass rate as a percentage, then put the percentages in order.
- Class A. Part over whole, times 100.13 ÷ 20 × 100 = 65%
- Class B. 20 ÷ 32 × 100 = 62.5%
- Class C. 17 ÷ 25 × 100 = 68%
- Put in order, highest first. 68 is bigger than 65, which is bigger than 62.5.C (68%), A (65%), B (62.5%)
Check. As decimals: 0.68, 0.65, 0.625, which goes down each time. ✓
Watch out. Compare the percentages, not the numbers who passed.
Method. To write one quantity as a percentage of another: write it as a fraction (part over whole), then change the fraction into a percentage.
- Write the part over the whole as a fraction. A percentage compares a part with the whole. Both numbers must be in the same units.35,00028,000
- Divide the top by the bottom. This changes the fraction into a decimal.35,000 ÷ 28,000 = 1.25
- Multiply by 100. To change a decimal into a percentage multiply by 100, because a percentage is a number out of 100.1.25 × 100 = 125%
Check. Check: 125% of 28,000 = 1.25 × 28,000 = 35,000, which is the part we started with. ✓
Watch out. Divide by the whole (the amount you are comparing with), not by the part.
Method. To write one quantity as a percentage of another: write it as a fraction (part over whole), then change the fraction into a percentage.
- Write the part over the whole as a fraction. A percentage compares a part with the whole. Both numbers must be in the same units.0.351.4
- Divide the top by the bottom. This changes the fraction into a decimal.0.35 ÷ 1.4 = 0.25
- Multiply by 100. To change a decimal into a percentage multiply by 100, because a percentage is a number out of 100.0.25 × 100 = 25%
Check. Check: 25% of 1.4 = 0.25 × 1.4 = 0.35, which is the part we started with. ✓
Watch out. Divide by the whole (the amount you are comparing with), not by the part.
Method. To write one quantity as a percentage of another: write it as a fraction (part over whole), then change the fraction into a percentage.
- Write the part over the whole as a fraction. A percentage compares a part with the whole. Both numbers must be in the same units.7.24.5
- Divide the top by the bottom. This changes the fraction into a decimal.7.2 ÷ 4.5 = 1.6
- Multiply by 100. To change a decimal into a percentage multiply by 100, because a percentage is a number out of 100.1.6 × 100 = 160%
Check. Check: 160% of 4.5 = 1.6 × 4.5 = 7.2, which is the part we started with. ✓
Watch out. Divide by the whole (the amount you are comparing with), not by the part.
Method. Find an example where the part is bigger than the whole you compare with.
- Choose two numbers. Make the first bigger than the second, for example 30 and 20.30 compared with 20
- Write 30 as a percentage of 20. Part over whole, times 100.30 ÷ 20 × 100 = 150%
- Explain. A percentage is more than 100% whenever the first amount is bigger than the amount it is compared with.Chen is wrong: 30 is 150% of 20.
Check. 150% of 20 = 1.5 × 20 = 30. ✓
Watch out. Percentages above 100% are normal when a quantity has grown.