OCR GCSE Mathematics: Fractions and decimal fractions (J560) – 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 sections 2.01 Fractions and 2.02 Decimal fractions of OCR GCSE (9-1) Mathematics, J560, in Version 2.1 of the specification (August 2026). Everything is for both tiers except question 8, which tests recurring decimals and exact fractions and is Higher tier only. Attempt every question by hand: the specification asks for the decimal skills in section 2.02 without a calculator, and Paper 2 and Paper 5 do not allow one.

Read the study guide or the revision notes first. The OCR GCSE Mathematics hub and the printable checklist cover the whole course. For percentages and mixed topic questions, see the fractions, decimals and percentages practice. A free 10-minute diagnostic can show where your gaps are.

Questions

1. (a) Write 84/126 in its simplest form. [2] (b) Write 6 5/8 as an improper fraction. [1]

2. Work out 7/12 + 4/9. Give your answer as a mixed number. [3]

3. Work out 4 1/2 − 2 7/8. Give your answer as a mixed number. [3]

4. (a) Work out 5/14 × 7/10. [2] (b) Work out −2 1/4 ÷ 1 1/2. [3]

5. (a) Find 5/9 of £8.10. [2] (b) A bag of flour holds 1.2 kg. A baker uses 450 g. Write the amount used as a fraction of the bag, in its simplest form. [3] (c) A farmer feeds the animals 9/4 of a 52 kg sack each week. How many kilograms is that? [2]

6. (a) Write 0.28 as a fraction in its simplest form. [2] (b) Write 13/16 as a decimal, showing your method. [3]

7. Use division to write 7/12 as a decimal. Show that the decimal recurs and write your answer using the word “recurring”. [3]

8. (Higher tier only) (a) Write 0.151515… (15 recurring) as a fraction in its simplest form. [2] (b) Show that 0.41111… (1 recurring) = 37/90. [3] (c) Write 7/33 as a recurring decimal. [2]

9. (a) Work out 12.7 − 4.86. [2] (b) Work out −3.2 × 0.15. [3] (c) Work out −0.6 − (−1.35). [2]

10. (a) Work out 0.84 ÷ 7. [2] (b) Work out 5.76 ÷ 0.24. [3] (c) Work out −1.8 ÷ 0.4. [2]

11. A roll of ribbon is 7.5 m long. A florist uses 3/5 of the roll for a banner. (a) Find the length of the banner. [2] (b) The rest of the ribbon is cut into pieces that are each 0.45 m long. How many whole pieces can be cut, and how much ribbon is left over? [5]

12. A water tank is 3/8 full. After 2 1/4 litres are added, it is 5/8 full. (a) Work out the capacity of the tank. [4] (b) Work out the volume of water in the tank now. Give your answer as a mixed number of litres. [2]

Answers

1. (a) The highest common factor of 84 and 126 is 42. Dividing both by 42 (or by smaller factors in steps) [1] gives 2/3 [1] [2] (b) 6 × 8 + 5 = 53, so 53/8 [1] [1] Examiner insight: Dividing in several small steps is fine if you finish at a fraction with no common factor left; stopping at 14/21 would leave the answer unsimplified.

2. The lowest common denominator is 36 [1]. 7/12 = 21/36 and 4/9 = 16/36, so the sum is 37/36 [1]. As a mixed number this is 1 1/36 [1] [3] Examiner insight: Show both converted fractions. If you slip on the final conversion, the earlier lines still show your method.

3. 4 1/2 = 9/2 and 2 7/8 = 23/8 [1]. Over eighths: 36/8 − 23/8 [1] = 13/8 = 1 5/8 [1] [3] Examiner insight: Converting to improper fractions avoids borrowing. Subtracting the whole numbers and the fractions separately gives 1/2 − 7/8, which is negative, and this is where many slips begin.

4. (a) Cancel the 7 with the 14 and the 5 with the 10: (1 × 1)/(2 × 2) [1] = 1/4 [1] [2] (b) −2 1/4 = −9/4 and 1 1/2 = 3/2, so the calculation is −9/4 ÷ 3/2 [1]. Multiply by the reciprocal: −9/4 × 2/3 [1] = −18/12 = −3/2 or −1 1/2 [1] [3] Examiner insight: Convert the mixed numbers before you do anything else, and keep the minus sign with the whole of −2 1/4, not just the 2.

5. (a) £8.10 ÷ 9 = £0.90 [1], then × 5 = £4.50 [1] [2] (b) Use the same units: 1.2 kg = 1200 g [1]. The fraction is 450/1200 [1]. Dividing by 150 gives 3/8 [1] [3] (c) 52 ÷ 4 = 13 [1], and 13 × 9 = 117 kg [1] [2] Examiner insight: Part (b) needs both quantities in the same unit before you write the fraction. A comment that the answer in (c) is more than 52 kg shows you have checked it makes sense for a fraction greater than 1.

6. (a) 0.28 = 28/100 [1] = 7/25 [1] [2] (b) Divide 13 by 16: 130 ÷ 16 = 8 remainder 2, 20 ÷ 16 = 1 remainder 4, 40 ÷ 16 = 2 remainder 8, 80 ÷ 16 = 5 exactly [1]. Digits 8, 1, 2, 5 [1]. So 13/16 = 0.8125 [1] [3] Examiner insight: If the question says “showing your method”, the division layout is part of the answer. A decimal on its own is a risk if it is wrong.

7. Divide 7 by 12: 70 ÷ 12 = 5 remainder 10 [1]. 100 ÷ 12 = 8 remainder 4, then 40 ÷ 12 = 3 remainder 4 [1]. The remainder 4 repeats, so the 3 repeats forever and 7/12 = 0.58333…, which is 0.58 with the 3 recurring [1] [3] Examiner insight: Say why it recurs: a remainder has come back. Writing out 0.58333 and stopping gives no evidence of the repeating pattern.

8. (Higher tier only) (a) Let x = 0.151515…. Then 100x = 15.151515… [1]. Subtracting gives 99x = 15, so x = 15/99 = 5/33 [1] [2] (b) Let x = 0.41111…. Then 10x = 4.1111… and 100x = 41.1111… [1]. Subtracting: 90x = 37 [1], so x = 37/90 as required [1] [3] (c) 7/33 = 21/99 [1], so the decimal is 0.212121… (21 recurring) [1] [2] Examiner insight: On a “show that” question, write the result you are proving as your last line, and make sure the multiples of x you subtract have the same repeating part.

9. (a) Write 12.70 − 4.86 with the points lined up [1]. The answer is 7.84 [1] [2] (b) 32 × 15 = 480 [1]. Together the factors have 3 decimal places, so the size is 0.480 [1]. The signs are different, so the answer is −0.48 [1] [3] (c) Subtracting a negative is adding: −0.6 + 1.35 [1] = 0.75 [1] [2] Examiner insight: Write the sign decision as its own line. In part (c), a common slip is to treat −(−1.35) as −1.35.

10. (a) 84 ÷ 7 = 12 [1], and 0.84 has two decimal places, so 0.12 [1] [2] (b) Multiply both numbers by 100 [1] to get 576 ÷ 24 [1] = 24 [1] [3] (c) Multiply both numbers by 10 to get −18 ÷ 4 [1] = −4.5 [1] [2] Examiner insight: Scale both numbers by the same power of 10. Scaling only the divisor changes the answer.

11. (a) 7.5 ÷ 5 = 1.5 [1], and 1.5 × 3 = 4.5 m [1] [2] (b) The rest is 7.5 − 4.5 = 3.0 m [1]. Pieces: 3.0 ÷ 0.45 = 300 ÷ 45 [1] = 6.66… [1], so 6 whole pieces [1]. These use 6 × 0.45 = 2.7 m, so 0.3 m is left over [1] [5] Examiner insight: For a “how many whole pieces” question, round down and say so. Rounding 6.66… up to 7 would need more ribbon than the florist has.

12. (a) The extra water fills 5/8 − 3/8 = 2/8 = 1/4 of the tank [1]. So 2 1/4 = 9/4 litres is 1/4 of the capacity [1]. Capacity = 9/4 ÷ 1/4 = 9/4 × 4 [1] = 9 litres [1] [4] (b) 5/8 of 9 = 45/8 [1] = 5 5/8 litres [1] [2] Examiner insight: Find the fraction that the added water represents before you try to find the capacity. This question is easy to start wrongly by finding 5/8 of 2 1/4.

Where marks are usually lost

• Combining fractions with different denominators before a common denominator is found, or adding the denominators too.
• Leaving a fraction unsimplified, or not giving a mixed number when the question asks for one.
• Multiplying or dividing mixed numbers without writing them as improper fractions first.
• Losing or misplacing a minus sign in a negative fraction or negative decimal.
• Writing one quantity as a fraction of another without matching units first.
• Misplacing the decimal point in a product. Count the decimal places in both factors.
• Multiplying the divisor by a power of 10 but forgetting to multiply the other number.
• Writing a recurring decimal as a truncated decimal, or putting the wrong number of 9s in the denominator.
• Rounding up when a question asks for the number of whole pieces.
• Giving a bare answer when the question says “show”, with no working to support it.

Next steps

• Recap with the revision notes.
• Return to the study guide for any skill that went wrong.
• Visit the OCR GCSE Mathematics hub and the printable checklist.
• Use the free 10-minute diagnostics to choose your next topic.
• Book a free trial class for help from a teacher.

Official syllabus

OCR, GCSE (9-1) Mathematics J560 specification, Version 2.1 (August 2026), for first assessment in 2017, sections 2.01 Fractions and 2.02 Decimal fractions. Published by OCR (Oxford Cambridge and RSA).