Edexcel International GCSE Mathematics A 4MA1: Fractions and decimals – 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 1.2 Fractions and 1.3 Decimals of Topic 1, Numbers and the number system, in the Pearson Edexcel International GCSE Mathematics A (4MA1) specification, Issue 2 (November 2017), for the January and June series examined on that specification. Section 1.2 and the Foundation content of 1.3 are for both tiers. Questions marked (Higher) test converting recurring decimals into fractions, which the specification lists as Higher tier only. A calculator is allowed on every 4MA1 paper, but where a question says “show your working” or “show that”, the written method earns the marks.

Before you start, read the fractions and decimals study guide or the revision notes. For mixed Topic 1 questions on ratio, percentages, standard form and bounds, use the Numbers and the number system practice questions. The Edexcel IGCSE Mathematics course hub and the printable checklist cover the whole course.

Questions

1. Write 54/90 in its simplest form. [2]

2.

(a) Write 29/6 as a mixed number. [1] (b) Write 3 4/9 as an improper fraction. [1]

3. Write these numbers in order of size, smallest first. [3]

0.62, 5/8, 0.6̇, 11/18

4. Show your working clearly. Give each answer as a mixed number in its simplest form.

(a) Work out 2 3/4 + 1 5/6. [3] (b) Work out 4 1/3 − 2 4/5. [3]

5.

(a) Show that 1 7/8 × 2 2/5 = 4 1/2. [3] (b) Work out 2 2/3 ÷ 1 1/9. Show your working and give your answer as a mixed number in its simplest form. [3]

6. A school has 840 students. 3/7 of the students are in the lower school. 5/12 of the lower-school students walk to school.

(a) Calculate how many lower-school students walk to school. [3] (b) 230 upper-school students also walk to school. Write the total number of students who walk to school as a fraction of all 840 students. Give your answer in its simplest form. [2] (c) Calculate the percentage of all the students who are lower-school students who walk. Give your answer to 1 decimal place. [2]

7.

(a) Write 7/20 as a decimal and as a percentage. [2] (b) Write 7/12 as a recurring decimal, using dot notation. [1] (c) Write 1.45 as a fraction in its simplest form and as a percentage. [2]

8.

(a) Write down the value of the digit 7 in the number 3.0472. [1] (b) Write these decimals in order of size, smallest first: 0.307, 0.37, 0.3, 0.073, 0.317 [2]

9.

(a) Complete the statement: 9 ÷ 4 = 9 × ___ [1] (b) Explain why dividing a number by 0.2 gives the same result as multiplying it by 5. [2] (c) Work out 3/4 ÷ 6 by multiplying by a unit fraction. Give your answer in its simplest form. [2]

10. (Higher) Prove algebraically that the recurring decimal 0.15̇ can be written as 7/45. [3]

11. (Higher) x = 0.4̇5̇ and y = 0.36̇.

(a) Write x as a fraction in its simplest form. [3] (b) Hence work out x ÷ 2 3/11, giving your answer in its simplest form. [2] (c) Show that y = 11/30. [3]

12. A water tank holds 480 litres when full. It starts the week full. On Monday, 2/5 of the full tank is used. On Tuesday, 3/4 of the water left in the tank is used.

(a) Calculate the fraction of a full tank used on Tuesday. [2] (b) Calculate the fraction of a full tank left at the end of Tuesday. [2] (c) Calculate how many litres are left at the end of Tuesday. [1] (d) Write the amount left at the end of Tuesday as a percentage of a full tank. [1] (e) On Wednesday, 1/6 of a full tank of water is added. Calculate the fraction of the tank that is now full, and the number of litres in the tank. [3]

Answers

1. Divide numerator and denominator by a common factor, for example 54/90 = 27/45 = 9/15, or by the HCF 18 [1]; 3/5 [1] [2] Examiner insight: A partly cancelled fraction such as 9/15 earns the method mark only; the accuracy mark needs the fraction in its lowest terms.

2. (a) 29 ÷ 6 = 4 remainder 5, so 4 5/6 [1] (b) 3 × 9 + 4 = 31, so 31/9 [1] Examiner insight: One-mark parts have no method mark, so check by converting back (4 × 6 + 5 = 29) before moving on.

3. 5/8 = 0.625 [1]; 11/18 = 0.6111… [1]; 11/18, 0.62, 5/8, 0.6̇ [1] [3] Examiner insight: The final mark needs the numbers written in their original form; a list of decimals (0.611, 0.62, 0.625, 0.666) does not answer the question as set.

4. (a) 2 3/4 = 11/4 and 1 5/6 = 11/6 [1]; 33/12 + 22/12 [1]; = 55/12 = 4 7/12 [1] (b) 4 1/3 = 13/3 and 2 4/5 = 14/5 [1]; 65/15 − 42/15 [1]; = 23/15 = 1 8/15 [1] Examiner insight: When the question says “show your working”, a correct answer copied from a calculator’s fraction key with no common-denominator line can score nothing, so write the converted fractions.

5. (a) 15/8 × 12/5 [1]; cancel 15 and 5 by 5: 3/8 × 12/1 = 36/8 [1]; = 9/2 = 4 1/2 [1] (b) 8/3 ÷ 10/9 [1]; = 8/3 × 9/10 [1]; = 72/30 = 12/5 = 2 2/5 [1] Examiner insight: On a “show that” the given answer 4 1/2 earns nothing on its own; the marks are for the improper fractions and an unsimplified product such as 36/8 or 180/40 before the final line.

6. (a) Lower school = 840 ÷ 7 × 3 = 360 [1]; walkers = 360 ÷ 12 × 5 [1]; = 150 [1] (b) 150 + 230 = 380, giving 380/840 [1]; = 19/42 [1] (c) 150/840 × 100 [1]; = 17.857…% = 17.9% [1] Examiner insight: Parts (b) and (c) can usually earn follow-through marks from a wrong answer to (a), but only when the method using that answer is written down.

7. (a) 0.35 [1]; 35% [1] (b) 7 ÷ 12 = 0.58333…, so 0.583̇ [1] (c) 145/100 = 29/20 (or 1 9/20) [1]; 145% [1] Examiner insight: In (b) the dot goes over the 3 only; 0.5̇83̇ would mean 0.583583…, a different number, and loses the mark.

8. (a) 7 thousandths (7/1000 or 0.007) [1] (b) Decimals padded to 0.307, 0.370, 0.300, 0.073, 0.317, or four of the five in the correct order [1]; 0.073, 0.3, 0.307, 0.317, 0.37 [1] Examiner insight: “7” alone does not answer (a); the mark needs the place value, as a word, fraction or decimal.

9. (a) 1/4 [1] (b) 0.2 = 1/5 [1]; dividing by 1/5 is the same as multiplying by its reciprocal, 5, because 1/5 × 5 = 1 [1] (c) 3/4 × 1/6 [1]; = 3/24 = 1/8 [1] Examiner insight: An “explain” mark needs the reason, not just an example; showing 10 ÷ 0.2 = 50 and 10 × 5 = 50 illustrates the fact but does not explain it.

10. Let x = 0.1555…; 10x = 1.555… and 100x = 15.555… [1]; 100x − 10x: 90x = 14 [1]; x = 14/90 = 7/45 [1] [3] Examiner insight: “Prove algebraically” needs the two multiples and the subtraction written out; checking that 7 ÷ 45 = 0.1555… works backwards and earns no marks.

11. (a) 100x = 45.4545… [1]; 100x − x: 99x = 45 [1]; x = 45/99 = 5/11 [1] (b) 5/11 ÷ 25/11 = 5/11 × 11/25 [1]; = 5/25 = 1/5 [1] (c) 10y = 3.666… and 100y = 36.666… [1]; 90y = 33 [1]; y = 33/90 = 11/30 [1] Examiner insight: “Hence” in (b) means use your answer from (a); a decimal calculation with 0.4545… does not use the fraction and may not earn the method mark.

12. (a) Left after Monday = 1 − 2/5 = 3/5 [1]; Tuesday = 3/4 × 3/5 = 9/20 [1] (b) 3/5 − 9/20 = 12/20 − 9/20 [1]; = 3/20 [1] (c) 3/20 × 480 = 72 litres [1] (d) 3/20 = 15% [1] (e) 3/20 + 1/6 = 9/60 + 10/60 [1]; = 19/60 [1]; 19/60 × 480 = 152 litres [1] Examiner insight: In (a), 3/4 is a fraction of what was left, not of the full tank; using 3/4 of 480 = 360 litres loses both marks in (a) and carries the error through.

Where marks are usually lost

• Adding denominators (2 3/4 + 1 5/6 written as 3 8/10).
• Stopping at a partly simplified fraction such as 9/15 or 72/30.
• Multiplying or dividing mixed numbers without converting to improper fractions.
• Flipping the first fraction instead of the second when dividing.
• Leaving an ordering answer as decimals instead of the numbers given.
• Writing only a digit (such as 7) when the question asks for its value.
• Taking a fraction of the whole amount when the question says “of what was left”.
• Placing recurring dots over the wrong digits (Higher).
• Working backwards from the given fraction on a “prove” question (Higher).

Next steps

• Refresh the facts: fractions and decimals revision notes
• Re-learn anything you missed: fractions and decimals study guide
• The whole of Topic 1: Numbers and the number system study guide and revision notes
• Course hub: Edexcel IGCSE Mathematics
• Track coverage: printable checklist
• Check other topics: all free 10-minute diagnostics
• Want help from a teacher? Book a free trial class

Official syllabus

Pearson Edexcel International GCSE in Mathematics (Specification A) (4MA1), Specification, Issue 2, November 2017, Pearson Education Limited (first assessment June 2018). Topic 1, Numbers and the number system, sections 1.2 Fractions and 1.3 Decimals (Foundation Tier content, and Higher Tier statement 1.3A).