Fractions, Decimals and Percentages

A joiner cuts a piece 1 1/2 m long and a piece 3/4 m long from a plank that is 3 m long. How much of the plank is left?

• A2 1/4 m
• B1 1/4 m
• C1 1/3 m
• D3/4 m✓

Answer: The two pieces total 1 1/2 + 3/4 = 1 2/4 + 3/4 = 2 1/4 m. The length left is 3 - 2 1/4 = 3/4 m. The amount used, 2 1/4 m, is what the joiner cut off, not what remains.

A football team won 18 of the 27 matches it played this season. What percentage of its matches did it win, to 1 decimal place?

• A150.0%
• B33.3%
• C66.7%✓
• D66.6%

Answer: 18 out of 27 is 18 ÷ 27 = 0.6666..., which is 66.666...%. The next digit after the first decimal place is 6, so it rounds up to 66.7%. Cutting the digits off without rounding gives 66.6%, and 33.3% is the share of matches not won.

Four learners compare their test results. Asha scored 17/20, Ben scored 0.83 of the marks, Cara scored 84% and Dev scored 5/6 of the marks. Who scored the highest proportion of the marks?

• ADev, with 5/6
• BCara, with 84%
• CBen, with 0.83
• DAsha, with 17/20✓

Answer: Change them all to decimals: 17/20 = 0.85, 0.83 stays as 0.83, 84% = 0.84 and 5/6 = 0.833... The largest is 0.85, so Asha scored the highest proportion.

A recipe needs 1/2 kg of flour for the pastry and 1/3 kg for the topping. The cook opens a full 1 1/2 kg bag of flour. How much flour is left after making the recipe once?

• A1/6 kg
• B2/3 kg✓
• C1 1/10 kg
• D5/6 kg

Answer: Flour used: 1/2 + 1/3 = 3/6 + 2/6 = 5/6 kg. Flour left: 1 1/2 - 5/6 = 9/6 - 5/6 = 4/6 = 2/3 kg. Adding the fractions as 2/5 by adding tops and bottoms is a common error and leads to 1 1/10 kg.

Three shops sell the same £60 jacket. Shop A takes 2/5 off the price. Shop B takes 35% off. Shop C takes 0.45 of the price off but then adds £5 delivery. Which shop is cheapest?

• AShop C, at £33.00
• BShop C, at £38.00
• CShop B, at £39.00
• DShop A, at £36.00✓

Answer: Shop A: 2/5 of £60 is £24, so the price is £36. Shop B: 35% of £60 is £21, so £39. Shop C: 0.45 × £60 = £27 off gives £33, plus £5 delivery makes £38. Shop A is cheapest at £36; £33 forgets Shop C's delivery charge.

A group's restaurant bill is £250 before a 12% service charge is added. The group splits the total equally between 8 people. How much does each person pay?

• A£31.25
• B£32.75
• C£3.75
• D£35.00✓

Answer: 12% of £250 is 0.12 × 250 = £30, so the total is £280. Shared between 8 people: £280 ÷ 8 = £35.00. Adding £12 instead of 12% gives £32.75, and £31.25 leaves out the service charge.

After a 5% pay rise, Sam earns £26,250 a year. What was Sam's salary before the rise?

• A£25,000✓
• B£24,937.50
• C£27,562.50
• D£25,500

Answer: £26,250 is 105% of the old salary, so the old salary is £26,250 ÷ 1.05 = £25,000.

A coat is reduced by 30% in a sale and now costs £56. What was its original price?

• A£72.80
• B£39.20
• C£16.80
• D£80✓

Answer: £56 is 70% of the original price, so the original price is £56 ÷ 0.7 = £80.

A plumber's bill comes to £342 including VAT at 20%. What is the bill before VAT is added?

• A£273.60
• B£410.40
• C£285✓
• D£68.40

Answer: £342 is 120% of the price before VAT, so the price before VAT is £342 ÷ 1.2 = £285.

A repair costs £588 including VAT at 20%. How much of that total is VAT?

• A£117.60
• B£98✓
• C£147
• D£490

Answer: The total is 120% of the price before VAT, so the VAT is 20 parts out of 120, which is one sixth of the total: £588 ÷ 6 = £98.

A monthly gas bill has gone up by 8% and is now £129.60. What was the bill before the increase?

• A£119.23
• B£139.97
• C£120✓
• D£116.64

Answer: £129.60 is 108% of the old bill, so the old bill is £129.60 ÷ 1.08 = £120.

With a 15% staff discount, a laptop costs £527. What is its full price?

• A£606.05
• B£620✓
• C£447.95
• D£79.05

Answer: £527 is 85% of the full price, so the full price is £527 ÷ 0.85 = £620.

In a survey, 36 people said they cycle to work. That is 24% of everyone asked. How many people were asked altogether?

• A150✓
• B144
• C60
• D8.64

Answer: 36 is 24% of the total, so the total is 36 ÷ 0.24 = 150 people.

A price on a receipt includes VAT at 20%. Which calculation gives the price before VAT?

• AMultiply the total by 0.8
• BMultiply the total by 1.2
• CDivide the total by 20 and subtract it
• DDivide the total by 1.2✓

Answer: Adding VAT at 20% multiplies a price by 1.2, so the price before VAT is found by dividing the total by 1.2.

A town's population rose from 48,000 to 52,320. What was the percentage increase?

• A8.3%
• B9%✓
• C4.3%
• D90%

Answer: Increase: 52,320 - 48,000 = 4,320. Percentage increase = increase ÷ original × 100 = 4,320 ÷ 48,000 × 100 = 9%. Dividing by the new population (52,320) instead gives about 8.3%.

A car bought for £16,500 is sold two years later for £11,880. What is the percentage decrease in its value?

• A72%
• B38.9%
• C28%✓
• D14%

Answer: Decrease: £16,500 - £11,880 = £4,620. Percentage decrease = £4,620 ÷ £16,500 × 100 = 28%. 72% is the percentage of the value that is left, and 38.9% divides by the selling price instead of the original price.

In a quiz, Mo answers 42 of the 56 questions correctly. What fraction of the questions did he get right, in its simplest form?

• A1/4
• B3/4✓
• C4/3
• D6/7

Answer: The fraction is 42/56. Both numbers divide by 14: 42 ÷ 14 = 3 and 56 ÷ 14 = 4, giving 3/4. 1/4 is the fraction he got wrong, and 4/3 is the fraction upside down, which is more than a whole quiz.

A carpenter cuts lengths of 0.875 m, 1.25 m and 0.635 m from a plank that is 3 m long. How much of the plank is left?

• A0.14 m
• B0.24 m✓
• C2.76 m
• D0.34 m

Answer: Add the lengths, lining up the decimal points: 0.875 + 1.250 + 0.635 = 2.760 m. The plank left is 3.000 - 2.760 = 0.240 m, or 0.24 m. 2.76 m is the total cut off, not what remains.

The price of fuel was £1.60 a litre. It rose by 10% one month, then fell by 10% the next month. What is the price now, to the nearest penny?

• A£1.58✓
• B£1.76
• C£1.44
• D£1.60

Answer: After the rise: £1.60 × 1.1 = £1.76. After the fall: £1.76 × 0.9 = £1.584, which is £1.58 to the nearest penny. The 10% fall is taken from the larger price, so it takes off more than the rise added, and the price does not return to £1.60.