AQA GCSE Mathematics 8300: Fractions, decimals and percentages – Practice Questions

These are original questions written for Marlbridge, for revision and practice on this content. They are not reproduced past-paper questions, and they do not replicate the exam’s exact structure, question count or mark tariffs – examination boards hold copyright in their own papers. Use these alongside the official past papers from your board or school.

These questions cover section 3.1.2, Fractions, decimals and percentages (N10, N11 and N12), of the AQA GCSE Mathematics (8300) specification, version 1.0, for teaching from September 2015 with exams from May/June 2017 onwards. Questions on converting between recurring decimals and fractions are labelled (Higher), because that skill is Higher tier only; everything else suits both tiers. Each question says whether it is non-calculator (Paper 1 style) or calculator (Papers 2 and 3 style).

Learn the content first in the study guide and the revision notes. These questions are different from the topic-level Number practice questions, so use both. The course hub is AQA GCSE Mathematics and the printable checklist lists every statement.

Questions

1. (non-calculator)

(a) Write 0.35 as a fraction in its simplest form. [1] (b) Write 9/40 as a decimal. [1]

2. (non-calculator) Write these numbers in order of size. Start with the smallest.

17/25    0.7    69%    0.695    11/16 [2]

3. (non-calculator) Work out

(a) 3/8 of 72 [1] (b) 45% of 160 [2] (c) 135% of 60 [1]

4. (calculator)

(a) Write down the multiplier for an increase of 8%. [1] (b) A gym membership costs £42.50 per month. The cost increases by 8%. Work out the new monthly cost. [2] (c) A car is worth £14 600. Its value decreases by 22%. Use a multiplier to work out its new value. [2]

5. (non-calculator) A paint colour is made by mixing red, blue and yellow paint in the ratio 2 : 3 : 5.

(a) What fraction of the mixture is blue paint? [1] (b) The amount of red paint is what fraction of the amount of yellow paint? Give your answer in its simplest form. [1] (c) Lena makes 6 litres of the mixture. How much yellow paint does she use? [2]

6. (non-calculator) Amir and Beth share a bag of sweets. Amir gets 5/9 of the sweets. Amir gets 12 more sweets than Beth. How many sweets were in the bag? [3]

7. (non-calculator) A garden centre has 240 plants. 3/8 of the plants are shrubs and the rest are flowers. 2/5 of the shrubs and 1/3 of the flowers are in pots.

(a) What fraction of all the plants are in pots? Give your answer in its simplest form. [4] (b) How many plants are in pots? [1]

8. (Higher, non-calculator)

(a) Write 7/12 as a recurring decimal. Use dot notation. [2] (b) Show that 0.2̇7̇ = 3/11 [3]

9. (Higher, non-calculator) Write 0.40̇9̇ as a fraction in its simplest form. [3]

10. (Higher, non-calculator) x = 0.6̇ and y = 0.1̇5̇

(a) Write x and y as fractions in their simplest form. [2] (b) Work out x + y. Give your answer as a fraction in its simplest form. [1] (c) Write your answer to (b) as a recurring decimal. [1]

11. (calculator) A shop buys 400 phone cases at £3.20 each. It sells 3/5 of the cases at £7.50 each. It sells the rest in a sale at 40% off the £7.50 price.

The manager says, “Our total income from the cases is more than double what we paid for them.”

Is the manager correct? Show your working. [6]

12. (calculator) A colony of 2400 birds increases by 1/6 in the first year. In the second year the number decreases by 15%. In the third year it increases by 5%.

(a) Work out the single multiplier that gives the overall change over the three years. Give it as an exact decimal. [2] (b) Work out the number of birds after three years. [1] (c) Work out the overall percentage change over the three years. [2]

Answers

1. (a) 35/100 = 7/20 [1] (b) 9/40 = 225/1000 = 0.225 [1] Examiner insight: “Simplest form” means fully cancelled; 35/100 on its own would not earn the mark in (a).

2. Converts to decimals with the same places: 0.6800, 0.7000, 0.6900, 0.6950, 0.6875 [1]. Order: 17/25, 11/16, 69%, 0.695, 0.7 [1] Examiner insight: One mark is usually given for correct conversions even if the order slips, but the final mark needs the original values in the right order, not your decimals.

3. (a) 72 ÷ 8 × 3 = 27 [1] (b) 10% = 16, so 40% = 64 and 5% = 8 [1]; 64 + 8 = 72 [1] (c) 100% = 60 and 35% = 21, so 135% = 81 [1] Examiner insight: On a non-calculator paper, the method mark in (b) comes from showing the building blocks (10%, 5%), so write them down.

4. (a) 1.08 [1] (b) 42.50 × 1.08 [1] = £45.90 [1] (c) Multiplier 1 − 0.22 = 0.78 [1]; 14 600 × 0.78 = £11 388 [1] Examiner insight: Write money to two decimal places when pence are involved; £45.9 is usually penalised on the accuracy mark.

5. (a) 2 + 3 + 5 = 10 parts, so blue = 3/10 [1] (b) red/yellow = 2/5, so 2/5 [1] (c) Yellow = 5/10 of the mixture [1]; 1/2 × 6 = 3 litres [1] Examiner insight: In (b) the denominator is the yellow share (5), not the total (10); 2/10 scores nothing.

6. Amir gets 5/9, so Beth gets 4/9, and Amir : Beth = 5 : 4 [1]. The difference is 1 part = 12 sweets [1]. Total = 9 parts = 9 × 12 = 108 sweets [1] Examiner insight: A check (Amir 60, Beth 48, difference 12) is quick and catches the 5 : 9 error before you lose the method marks.

7. (a) Flowers = 1 − 3/8 = 5/8 [1]. Shrubs in pots = 2/5 × 3/8 = 3/20; flowers in pots = 1/3 × 5/8 = 5/24 [1]. 3/20 + 5/24 = 18/120 + 25/120 [1] = 43/120 [1] (b) 43/120 × 240 = 86 [1] Examiner insight: In (b) follow-through is normally allowed from a wrong fraction in (a), so finish the calculation even if you doubt (a).

8. (a) 7 ÷ 12 = 0.58333… [1] = 0.583̇ [1] (b) Let x = 0.272727…; then 100x = 27.272727… [1]. Subtract: 99x = 27 [1]. x = 27/99 = 3/11 [1] Examiner insight: On a “show that”, every line must be written, including the subtraction; writing only 27/99 = 3/11 gets at most one mark.

9. Let x = 0.4090909…; 10x = 4.090909… and 1000x = 409.090909… [1]. Subtract: 990x = 405 [1]. x = 405/990 = 9/22 [1] Examiner insight: The two equations you subtract must have identical recurring tails; 100x and x do not line up here, and that method earns no marks.

10. (a) x = 6/9 = 2/3 [1]; y = 15/99 = 5/33 [1] (b) 22/33 + 5/33 = 27/33 = 9/11 [1] (c) 0.8̇1̇ (0.818181…) [1] Examiner insight: Part (c) needs dot notation on both repeating digits, or the decimal written with enough repeats to show the pattern.

11. Cost = 400 × 3.20 = £1280 [1]. Full-price cases = 3/5 × 400 = 240 [1]; income = 240 × 7.50 = £1800 [1]. Sale price = 7.50 × 0.6 = £4.50 [1]; income = 160 × 4.50 = £720 [1]. Total = £2520, but double the cost is £2560, so the manager is not correct (£40 short) [1] Examiner insight: The final mark needs a decision backed by the two figures being compared; “No” on its own, or a correct total with no comparison, does not earn it.

12. (a) 7/6 × 0.85 × 1.05 [1] = 1.04125 [1] (b) 2400 × 1.04125 = 2499 birds [1] (c) 1.04125 − 1 = 0.04125 [1], so a 4.125% increase [1] Examiner insight: Rounding 7/6 to 1.17 early gives a different number of birds; keep the exact fraction in the calculator until the end.

Where marks are usually lost

• Not cancelling a fraction fully when the question asks for its simplest form.
• Writing an ordered list as converted decimals instead of the original numbers.
• Reading 0.7 as smaller than 0.695 because 695 looks bigger.
• Using the total, not the other part, as the denominator in “what fraction of” ratio questions.
• Turning “Amir gets 5/9” into the ratio 5 : 9.
• Adding fractions of different groups without first multiplying by the group sizes.
• (Higher) Subtracting equations whose recurring tails do not match.
• (Higher) Leaving out steps on a “show that”.
• Rounding an intermediate multiplier and getting a final answer that is not exact.
• Giving a yes/no judgement without the two figures it depends on.

Next steps

• Fractions, decimals and percentages revision notes
• Fractions, decimals and percentages study guide
• Number revision notes
• AQA GCSE Mathematics course hub
• Printable checklist
• All free 10-minute diagnostics
• Book a free trial class

Official syllabus

AQA GCSE Mathematics (8300) specification, for teaching from September 2015, exams from May/June 2017, version 1.0, published by AQA – section 3.1.2 Fractions, decimals and percentages (N10, N11, N12).