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Percentages of amounts, sale prices, and working out what percentage one number is of another.
Question 1 of 12
200 children belong to the chess club. 160 of them came to the last session. What percentage of the members came?
Write it as a fraction of the whole first: 160 out of 200, or 160/200. To turn a fraction into a percentage, divide and multiply by 100: 160 ÷ 200 = 0.8, and 0.8 × 100 = 80%. The other way round — 200 ÷ 160 — answers a different question entirely. If the fraction simplifies to something with 100, 50, 25, 20 or 10 on the bottom, the percentage can be read straight off.
The answer is D. Write it as a fraction of the whole first: 160 out of 200, or 160/200. To turn a fraction into a percentage, divide and multiply by 100: 160 ÷ 200 = 0.8, and 0.8 × 100 = 80%. The other way round — 200 ÷ 160 — answers a different question entirely. If the fraction simplifies to something with 100, 50, 25, 20 or 10 on the bottom, the percentage can be read straight off.
A season ticket costs £73 at the leisure centre. The price goes up by 10%. What is the new price?
10% of £73 is £7.30, so that is the amount the price rises by. £73 + £7.30 = £80.30. Answering £7.30 is the trap — that is the increase, not the new price, and the question asks for the price. A quicker route: adding 10% gives 110%, and 110% of £73 is £80.30 in one step. Read the last line again before answering. Sale questions ask for the price far more often than for the discount.
The answer is B. 10% of £73 is £7.30, so that is the amount the price rises by. £73 + £7.30 = £80.30. Answering £7.30 is the trap — that is the increase, not the new price, and the question asks for the price. A quicker route: adding 10% gives 110%, and 110% of £73 is £80.30 in one step. Read the last line again before answering. Sale questions ask for the price far more often than for the discount.
A coat costs £41 at the department store. In the sale it is reduced by 30%. What is the sale price?
30% of £41 is £12.30, so that is the amount the price falls by. £41 − £12.30 = £28.70. Answering £12.30 is the trap — that is the discount, not the sale price, and the question asks for the price. A quicker route: taking 30% off leaves 70%, and 70% of £41 is £28.70 in one step. A sale price must be lower than the original. It sounds obvious, and it catches people under time pressure.
The answer is A. 30% of £41 is £12.30, so that is the amount the price falls by. £41 − £12.30 = £28.70. Answering £12.30 is the trap — that is the discount, not the sale price, and the question asks for the price. A quicker route: taking 30% off leaves 70%, and 70% of £41 is £28.70 in one step. A sale price must be lower than the original. It sounds obvious, and it catches people under time pressure.
80 children belong to the football team. 32 of them came to the last session. What percentage of the members came?
Write it as a fraction of the whole first: 32 out of 80, or 32/80. To turn a fraction into a percentage, divide and multiply by 100: 32 ÷ 80 = 0.4, and 0.4 × 100 = 40%. The other way round — 80 ÷ 32 — answers a different question entirely. The number you are asking about goes on top; the total goes underneath. Getting them the wrong way round is the usual error.
The answer is B. Write it as a fraction of the whole first: 32 out of 80, or 32/80. To turn a fraction into a percentage, divide and multiply by 100: 32 ÷ 80 = 0.4, and 0.4 × 100 = 40%. The other way round — 80 ÷ 32 — answers a different question entirely. The number you are asking about goes on top; the total goes underneath. Getting them the wrong way round is the usual error.
50 children belong to Scouts. 15 of them came to the last session. What percentage of the members came?
Write it as a fraction of the whole first: 15 out of 50, or 15/50. To turn a fraction into a percentage, divide and multiply by 100: 15 ÷ 50 = 0.3, and 0.3 × 100 = 30%. The other way round — 50 ÷ 15 — answers a different question entirely. If the fraction simplifies to something with 100, 50, 25, 20 or 10 on the bottom, the percentage can be read straight off.
The answer is B. Write it as a fraction of the whole first: 15 out of 50, or 15/50. To turn a fraction into a percentage, divide and multiply by 100: 15 ÷ 50 = 0.3, and 0.3 × 100 = 30%. The other way round — 50 ÷ 15 — answers a different question entirely. If the fraction simplifies to something with 100, 50, 25, 20 or 10 on the bottom, the percentage can be read straight off.
20 children belong to the school choir. 5 of them came to the last session. What percentage of the members came?
Write it as a fraction of the whole first: 5 out of 20, or 5/20. To turn a fraction into a percentage, divide and multiply by 100: 5 ÷ 20 = 0.25, and 0.25 × 100 = 25%. The other way round — 20 ÷ 5 — answers a different question entirely. Check against a landmark: is it more or less than half? The answer should agree.
The answer is D. Write it as a fraction of the whole first: 5 out of 20, or 5/20. To turn a fraction into a percentage, divide and multiply by 100: 5 ÷ 20 = 0.25, and 0.25 × 100 = 25%. The other way round — 20 ÷ 5 — answers a different question entirely. Check against a landmark: is it more or less than half? The answer should agree.
What is 60% of 800?
Start from 10%, which is just dividing by 10: 10% of 800 is 80. 60% is 6 lots of that: 80 × 6 = 480. Building percentages out of 10% and 5% is faster and safer than the formula, and it is how the question is meant to be done in the time allowed. 10% is divide by ten, 5% is half of that, 1% is divide by a hundred. Almost every percentage can be built from those three.
The answer is A. Start from 10%, which is just dividing by 10: 10% of 800 is 80. 60% is 6 lots of that: 80 × 6 = 480. Building percentages out of 10% and 5% is faster and safer than the formula, and it is how the question is meant to be done in the time allowed. 10% is divide by ten, 5% is half of that, 1% is divide by a hundred. Almost every percentage can be built from those three.
What is 75% of 400?
Start from 10%, which is just dividing by 10: 10% of 400 is 40. 5% is half of 10%, which is 20. 75% is 7 lots of 10% plus 5%: 280 + 20 = 300. Building percentages out of 10% and 5% is faster and safer than the formula, and it is how the question is meant to be done in the time allowed. 10% is divide by ten, 5% is half of that, 1% is divide by a hundred. Almost every percentage can be built from those three.
The answer is B. Start from 10%, which is just dividing by 10: 10% of 400 is 40. 5% is half of 10%, which is 20. 75% is 7 lots of 10% plus 5%: 280 + 20 = 300. Building percentages out of 10% and 5% is faster and safer than the formula, and it is how the question is meant to be done in the time allowed. 10% is divide by ten, 5% is half of that, 1% is divide by a hundred. Almost every percentage can be built from those three.
A season ticket costs £55 at the leisure centre. The price goes up by 25%. What is the new price?
25% of £55 is £13.75, so that is the amount the price rises by. £55 + £13.75 = £68.75. Answering £13.75 is the trap — that is the increase, not the new price, and the question asks for the price. A quicker route: adding 25% gives 125%, and 125% of £55 is £68.75 in one step. Working out what percentage is left, then taking that in one go, halves the work and the chances of slipping.
The answer is C. 25% of £55 is £13.75, so that is the amount the price rises by. £55 + £13.75 = £68.75. Answering £13.75 is the trap — that is the increase, not the new price, and the question asks for the price. A quicker route: adding 25% gives 125%, and 125% of £55 is £68.75 in one step. Working out what percentage is left, then taking that in one go, halves the work and the chances of slipping.
What is 20% of 720?
Start from 10%, which is just dividing by 10: 10% of 720 is 72. 20% is 2 lots of that: 72 × 2 = 144. Building percentages out of 10% and 5% is faster and safer than the formula, and it is how the question is meant to be done in the time allowed. Check the size: 20% of something should be about a fifth of it.
The answer is A. Start from 10%, which is just dividing by 10: 10% of 720 is 72. 20% is 2 lots of that: 72 × 2 = 144. Building percentages out of 10% and 5% is faster and safer than the formula, and it is how the question is meant to be done in the time allowed. Check the size: 20% of something should be about a fifth of it.
80 children belong to netball club. 48 of them came to the last session. What percentage of the members came?
Write it as a fraction of the whole first: 48 out of 80, or 48/80. To turn a fraction into a percentage, divide and multiply by 100: 48 ÷ 80 = 0.6, and 0.6 × 100 = 60%. The other way round — 80 ÷ 48 — answers a different question entirely. If the fraction simplifies to something with 100, 50, 25, 20 or 10 on the bottom, the percentage can be read straight off.
The answer is D. Write it as a fraction of the whole first: 48 out of 80, or 48/80. To turn a fraction into a percentage, divide and multiply by 100: 48 ÷ 80 = 0.6, and 0.6 × 100 = 60%. The other way round — 80 ÷ 48 — answers a different question entirely. If the fraction simplifies to something with 100, 50, 25, 20 or 10 on the bottom, the percentage can be read straight off.
What is 5% of 800?
Start from 10%, which is just dividing by 10: 10% of 800 is 80. 5% is half of 10%: half of 80 is 40. Building percentages out of 10% and 5% is faster and safer than the formula, and it is how the question is meant to be done in the time allowed. 50% is half, 25% is half again. Use the easy ones as stepping stones.
The answer is D. Start from 10%, which is just dividing by 10: 10% of 800 is 80. 5% is half of 10%: half of 80 is 40. Building percentages out of 10% and 5% is faster and safer than the formula, and it is how the question is meant to be done in the time allowed. 50% is half, 25% is half again. Use the easy ones as stepping stones.
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