IGCSE Maths 0580 Fractions, Decimals and Percentages Past Paper Questions and Worked Solutions

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IGCSE Maths (0580) · Number · 1.4

Every fractions, decimals and percentages question from 21 Cambridge IGCSE Mathematics (0580) past papers (May/June 2025 to May/June 2026), syllabus section 1.4. 28 questions covering Core and Extended tiers, ordered from Core to Extended. Each question is labelled with its question paper code (for example 0580/11/M/J/26) and every final answer matches the official Cambridge mark scheme. Try each question first, then click “Show solution” to check your working. This page is part of our IGCSE Maths 0580 Number past paper questions.

0580 Fractions, Decimals and Percentages past paper questions: Core (Papers 1 and 3)

13 marksCore

May/June 2026 · Paper 1 · 0580/11/M/J/26 · Q5

(a) Write 1⁄2 as a decimal.

(b) Write 9⁄10 as a percentage.

(c) Write 0.15 as a fraction in its simplest form.

Show solution
Part (a)
  1. A fraction means divide: 1 ÷ 2 = 0.5
Answer 0.5
Part (b)
  1. Make the denominator 100: 9⁄10 = 90⁄100.
  2. Per cent means out of 100, so 90⁄100 = 90%
Answer 90%
Part (c)
  1. 0.15 is 15 hundredths: 0.15 = 15⁄100.
  2. The HCF of 15 and 100 is 5. Divide top and bottom by 5: 15⁄100 = 3⁄20
Answer 3⁄20
22 marksCore

May/June 2026 · Paper 1 · 0580/12/M/J/26 · Q3

(a) Write 35% as a decimal. (b) Write 4⁄5 as a percentage.

Show solution
Part (a)
  1. Per cent means out of 100, so divide by 100.
  2. 35% = 35 ÷ 100 = 0.35
Answer 0.35
Part (b)
  1. Make the denominator 100: multiply top and bottom by 20.
  2. 4⁄5 = 80⁄100 = 80%
Answer 80%
33 marksCore

May/June 2026 · Paper 1 · 0580/12/M/J/26 · Q7

A rectangle is divided into 48 equal squares (12 by 4) and 22 of them are shaded.

0580/12 May/June 2026 Q7 – 12 by 4 rectangle of squares with 22 shaded

(a) Write down the fraction of the rectangle that is shaded, in its simplest form.

(b) Shade some more squares so that 1⁄6 of the rectangle is not shaded.

Show solution
Part (a)
  1. 22 of the 48 squares are shaded: 22⁄48.
  2. Divide top and bottom by 2 (their HCF): 22⁄48 = 11⁄24
Answer 11⁄24
Part (b)
  1. 1⁄6 of 48 = 48 ÷ 6 = 8 squares must stay unshaded.
  2. So 48 − 8 = 40 squares must be shaded.
  3. 22 are already shaded, so shade 40 − 22 = 18 more squares
Answer 18 more squares
43 marksCore

May/June 2026 · Paper 1 · 0580/13/M/J/26 · Q6

A book has 420 pages. Meg reads 14 pages each day. Meg has read 1⁄3 of the number of pages so far. Find how many days it will take Meg to finish reading the rest of the book.

Show solution
  1. Pages already read = 1⁄3 of 420 = 420 ÷ 3 = 140.
  2. Pages left = 420 − 140 = 280.
  3. Meg reads 14 pages a day, so days needed = 280 ÷ 14 = 20 days
Answer 20 days
52 marksCore

May/June 2026 · Paper 3 · 0580/32/M/J/26 · Q7

Sian uses 2.7 litres of paint to cover 3⁄5 of a wall. Work out the total amount of paint she uses to cover the whole wall.

Show solution
  1. 3⁄5 of the wall uses 2.7 litres, so 1⁄5 of the wall uses 2.7 ÷ 3 = 0.9 litres.
  2. The whole wall is 5⁄5, so it uses 5 × 0.9 = 4.5 litres
Answer 4.5 litres
61 markCore

May/June 2026 · Paper 3 · 0580/33/M/J/26 · Q10

Fill in the box to complete the statement: the fraction of the rectangle that is shaded is □/7.

0580/33 May/June 2026 Q10 – rectangle divided into equal parts with some shaded
Show solution
  1. The rectangle is split into 7 equal parts, so the denominator is 7.
  2. Count the shaded parts: there are 5.
  3. 5⁄7
Answer 5⁄7
72 marksCore

Feb/Mar 2026 · Paper 1 · 0580/12/F/M/26 · Q3

(a) Write 0.47 as a percentage. (b) Write 9⁄100 as a decimal.

Show solution
Part (a)
  1. To change a decimal to a percentage, multiply by 100.
  2. 0.47 × 100 = 47%
Answer 47%
Part (b)
  1. 9⁄100 is 9 hundredths. Hundredths is the second place after the decimal point.
  2. 9⁄100 = 0.09
Answer 0.09
82 marksCore

Feb/Mar 2026 · Paper 1 · 0580/12/F/M/26 · Q4

(a) A grid has 40 squares. Shade 3⁄10 of the squares on the grid.

(b) A target diagram has 7 of its regions shaded. Shade 3 more regions so that 1⁄5 of the total area is shaded.

0580/12 February/March 2026 Q4 – (a) a 10 by 4 grid and (b) a target of rings divided into regions, 7 shaded
Show solution
Part (a)
  1. 3⁄10 of 40 = 40 ÷ 10 × 3 = 4 × 3 = 12.
  2. Shade 12 squares
Answer 12 squares
Part (b)
  1. The regions in different rings are different sizes, so you must compare areas, not just count regions.
  2. Work out the area of one region in each ring, then find what still needs shading to make 1⁄5 of the whole area.
  3. Shade 2 more regions in the third-largest ring and 1 more region in the second-largest ring
0580/12 February/March 2026 Q4 solution – grid with 12 squares shaded and target with one fifth shaded
Answer 2 more regions in the third-largest ring and 1 more region in the second-largest ring
92 marksCore

Feb/Mar 2026 · Paper 3 · 0580/32/F/M/26 · Q8

Work out a fraction that is exactly half-way between 1⁄6 and 3⁄8.

Show solution
  1. Use a common denominator of 24: 1⁄6 = 4⁄24 and 3⁄8 = 9⁄24.
  2. The number half-way between two numbers is their mean: add them and divide by 2.
  3. 4⁄24 + 9⁄24 = 13⁄24.
  4. 13⁄24 ÷ 2 = 13⁄48
Answer 13⁄48
102 marksCore

Oct/Nov 2025 · Paper 1 · 0580/11/O/N/25 · Q20

Some students take a test. 75 of the students pass the test. This is 3⁄5 of the students who take the test. Work out how many students take the test.

Show solution
  1. 3⁄5 of the students is 75, so 3 parts = 75.
  2. One part (1⁄5) = 75 ÷ 3 = 25.
  3. All the students = 5 parts = 5 × 25 = 125
Answer 125
113 marksCore

Oct/Nov 2025 · Paper 1 · 0580/12/O/N/25 · Q6

(a) Write 3⁄4 as a decimal. (b) Write 9⁄100 as a percentage. (c) Write 143% as a decimal.

Show solution
Part (a)
  1. A fraction means divide: 3 ÷ 4 = 0.75
Answer 0.75
Part (b)
  1. Per cent means out of 100, so 9⁄100 = 9%
Answer 9%
Part (c)
  1. Divide the percentage by 100: 143 ÷ 100 = 1.43
Answer 1.43
122 marksCore

Oct/Nov 2025 · Paper 3 · 0580/31/O/N/25 · Q4

Draw a ring around the fractions which are not equivalent to 2⁄5: 6⁄15, 1⁄10, 16⁄80, 10⁄25, 5⁄2

Show solution
  1. Simplify each fraction and compare it with 2⁄5.
  2. 6⁄15: divide by 3 → 2⁄5 (equivalent).
  3. 1⁄10 cannot be simplified and is not 2⁄5.
  4. 16⁄80: divide by 16 → 1⁄5 (not equivalent).
  5. 10⁄25: divide by 5 → 2⁄5 (equivalent).
  6. 5⁄2 is the reciprocal of 2⁄5, not the same value.
  7. Not equivalent: 1⁄10, 16⁄80 and 5⁄2
Answer 1⁄10, 16⁄80 and 5⁄2
133 marksCore

Oct/Nov 2025 · Paper 3 · 0580/33/O/N/25 · Q3

(a) Write 0.25 as a fraction. (b) Write 1⁄2 as a percentage. (c) Write 7% as a decimal.

Show solution
Part (a)
  1. 0.25 = 25⁄100. Divide the top and bottom by 25: 1⁄4
Answer 1⁄4
Part (b)
  1. Per cent means out of 100. 1⁄2 = 50⁄100 = 50%
Answer 50%
Part (c)
  1. Divide by 100: 7 ÷ 100 = 0.07
Answer 0.07
142 marksCore

May/June 2025 · Paper 1 · 0580/11/M/J/25 · Q8

(a) Write 90% as a fraction in its simplest form.

(b) Write 3⁄100 as a decimal.

Show solution
Part (a)
  1. Per cent means “out of 100”: 90% = 90⁄100.
  2. Simplify by dividing top and bottom by 10: 90⁄100 = 9⁄10
Answer 9⁄10
Part (b)
  1. 3⁄100 means 3 hundredths. The hundredths column is the second place after the decimal point.
  2. 3⁄100 = 0.03
Answer 0.03
153 marksCore

May/June 2025 · Paper 1 · 0580/11/M/J/25 · Q24

Work out 11⁄3 + 13⁄4. Give your answer as a mixed number in its simplest form.

Show solution
  1. Change each mixed number to an improper fraction: 11⁄3 = 4⁄3 and 13⁄4 = 7⁄4.
  2. The lowest common denominator of 3 and 4 is 12: 4⁄3 = 16⁄12 and 7⁄4 = 21⁄12.
  3. Add the numerators: 16⁄12 + 21⁄12 = 37⁄12.
  4. 37 ÷ 12 = 3 remainder 1, so 37⁄12 = 31⁄12
Answer 31⁄12
162 marksCore

May/June 2025 · Paper 1 · 0580/12/M/J/25 · Q2

Write three-quarters as (a) a decimal (b) a percentage.

Show solution
Part (a)
  1. Three-quarters = 3⁄4, and a fraction means divide: 3 ÷ 4 = 0.75
Answer 0.75
Part (b)
  1. To change a decimal to a percentage, multiply by 100: 0.75 × 100 = 75%
Answer 75%
171 markCore

May/June 2025 · Paper 1 · 0580/12/M/J/25 · Q6

The diagram shows a rectangle made of 35 small squares (7 by 5). Shade 2⁄5 of the rectangle.

0580/12 May/June 2025 Q6 – rectangle grid of 7 by 5 squares
Show solution
  1. The rectangle has 7 × 5 = 35 small squares.
  2. 2⁄5 of 35 = 35 ÷ 5 × 2 = 7 × 2 = 14.
  3. Shade any 14 squares
Answer Shade any 14 squares
183 marksCore

May/June 2025 · Paper 1 · 0580/12/M/J/25 · Q21

Work out 27⁄9 × 11⁄5. Give your answer as a mixed number in its simplest form.

Show solution
  1. Change to improper fractions: 27⁄9 = 25⁄9 and 11⁄5 = 6⁄5.
  2. Cancel before multiplying: 25 and 5 share 5 (→ 5 and 1), 6 and 9 share 3 (→ 2 and 3).
  3. 5⁄3 × 2⁄1 = 10⁄3
  4. 10 ÷ 3 = 3 remainder 1, so the answer is 31⁄3
Answer 31⁄3
194 marksCore

May/June 2025 · Paper 1 · 0580/13/M/J/25 · Q1

(a) Write the number 70 000 000 in words.

(b)(i) Write down the value of the 5 in the number 0.25. Give your answer as a fraction.

(b)(ii) Find the value of the reciprocal of 0.25.

Show solution
Part (a)
  1. 70 000 000 = 70 × 1 000 000, and 1 000 000 is one million.
  2. In words: seventy million
Answer seventy million
Part (b)(i)
  1. Write the place values: 0.25 = 2 tenths + 5 hundredths. The 5 is in the hundredths column.
  2. Value of the 5 = 5⁄100, which simplifies to 5⁄100 = 1⁄20
Answer 5⁄100 = 1⁄20
Part (b)(ii)
  1. Change 0.25 to a fraction: 0.25 = 1⁄4.
  2. The reciprocal is the fraction turned upside down: 4⁄1 = 4
Answer 4
203 marksCore

May/June 2025 · Paper 1 · 0580/13/M/J/25 · Q24

Work out 31⁄2 − 14⁄7. Give your answer as a mixed number in its simplest form.

Show solution
  1. Change to improper fractions: 31⁄2 = 7⁄2 and 14⁄7 = 11⁄7.
  2. The lowest common denominator of 2 and 7 is 14: 7⁄2 = 49⁄14 and 11⁄7 = 22⁄14.
  3. Subtract: 49⁄14 − 22⁄14 = 27⁄14.
  4. 27 ÷ 14 = 1 remainder 13, so the answer is 113⁄14
Answer 113⁄14

0580 Fractions, Decimals and Percentages past paper questions: Extended (Papers 2 and 4)

214 marksExtended

May/June 2026 · Paper 2 · 0580/21/M/J/26 · Q13

(a) Work out 0.92̇4̇ − 0.213 (where 0.92̇4̇ = 0.924 242…). Give your answer as a decimal correct to 5 decimal places.

(b) Write 0.67̇ as a fraction.

Show solution
Part (a)
  1. Write the recurring decimal out to enough places: 0.924 242 42…
  2. Subtract: 0.924 242 42… − 0.213 = 0.711 242 42…
  3. Round to 5 decimal places: the 6th digit is 2, so round down.
  4. 0.71124
Answer 0.71124
Part (b)
  1. Let x = 0.6777…
  2. Multiply by 10: 10x = 6.777… Multiply by 100: 100x = 67.777…
  3. Subtract so the recurring 7s cancel: 100x − 10x = 67.777… − 6.777…, so 90x = 61.
  4. x = 61⁄90
Answer x = 61⁄90
223 marksExtended

May/June 2026 · Paper 2 · 0580/22/M/J/26 · Q10

Write 0.73̇ as a fraction, giving your answer in its simplest form.

Show solution
  1. Let x = 0.7333… Only the 3 recurs, starting in the second decimal place.
  2. Multiply by 10: 10x = 7.333… Multiply by 100: 100x = 73.333…
  3. Subtract so the recurring parts cancel: 100x − 10x = 73.333… − 7.333…, so 90x = 66.
  4. x = 66⁄90. Divide top and bottom by 6: 11⁄15
Answer 11⁄15
231 markExtended

May/June 2026 · Paper 4 · 0580/43/M/J/26 · Q1

Complete the statement: 4⁄7 = □⁄56

Show solution
  1. Look at the denominators: 7 × 8 = 56.
  2. Whatever you do to the bottom, do the same to the top: 4 × 8 = 32.
  3. 4⁄7 = 32⁄56, so the missing number is 32
Answer 32
242 marksExtended

Oct/Nov 2025 · Paper 2 · 0580/21/O/N/25 · Q11

Write 0.2̇4̇ (0.242 424…) as a fraction in its simplest form.

Show solution
  1. Let x = 0.242 424… The recurring block has 2 digits, so multiply by 100.
  2. 100x = 24.242 424…
  3. Subtract so the recurring parts cancel: 100x − x = 24, so 99x = 24.
  4. x = 24⁄99. Divide top and bottom by 3: 8⁄33
Answer 8⁄33
253 marksExtended

Oct/Nov 2025 · Paper 2 · 0580/23/O/N/25 · Q20

Work out 0.11̇4̇ + 0.2 (where 0.11̇4̇ = 0.114 141…). Give your answer as a fraction.

Show solution
  1. Add the decimals first: 0.114 141… + 0.2 = 0.314 141…
  2. Let x = 0.314 141… The recurring block “14” has 2 digits and starts after the first decimal place.
  3. Multiply by 10: 10x = 3.141 41… Multiply by 1000: 1000x = 314.141 41…
  4. Subtract so the recurring parts cancel: 1000x − 10x = 314.1414… − 3.1414…, so 990x = 311.
  5. x = 311⁄990
Answer 311⁄990
263 marksExtended

May/June 2025 · Paper 2 · 0580/21/M/J/25 · Q4

Work out. 5⁄6 − 2⁄3 × 3⁄8

Show solution
  1. Follow the order of operations: multiply before subtracting.
  2. 2⁄3 × 3⁄8 = 6⁄24 = 1⁄4.
  3. Now subtract with a common denominator of 12: 5⁄6 = 10⁄12 and 1⁄4 = 3⁄12.
  4. 10⁄12 − 3⁄12 = 7⁄12
Answer 7⁄12
273 marksExtended

May/June 2025 · Paper 2 · 0580/21/M/J/25 · Q7

Write the recurring decimal 0.26 (0.2666…) as a fraction. Give your answer in its simplest form.

Show solution
  1. Let x = 0.2666…
  2. Multiply by 10 so the recurring part starts right after the point: 10x = 2.666…
  3. Multiply by 100: 100x = 26.666…
  4. Subtract to remove the recurring part: 100x − 10x = 26.666… − 2.666…, so 90x = 24.
  5. x = 24⁄90. Divide top and bottom by 6: 4⁄15
Answer 4⁄15
282 marksExtended

May/June 2025 · Paper 2 · 0580/22/M/J/25 · Q14

Write 0.25 (0.2555…) as a fraction.

Show solution
  1. Let x = 0.2555… Only the 5 recurs, and it starts in the second decimal place.
  2. Multiply by 10: 10x = 2.555… Multiply by 100: 100x = 25.555…
  3. Subtract so the recurring parts cancel: 100x − 10x = 25.555… − 2.555…, so 90x = 23.
  4. x = 23⁄90
Answer 23⁄90

Question papers used on this page

All fractions, decimals and percentages questions above, listed by 0580 question paper code.

QP codeFile namePaperQuestions
0580/11/M/J/260580_s26_qp_11May/June 2026 · Paper 1 (Core)Q5
0580/12/M/J/260580_s26_qp_12May/June 2026 · Paper 1 (Core)Q3, Q7
0580/13/M/J/260580_s26_qp_13May/June 2026 · Paper 1 (Core)Q6
0580/21/M/J/260580_s26_qp_21May/June 2026 · Paper 2 (Extended)Q13
0580/22/M/J/260580_s26_qp_22May/June 2026 · Paper 2 (Extended)Q10
0580/32/M/J/260580_s26_qp_32May/June 2026 · Paper 3 (Core)Q7
0580/33/M/J/260580_s26_qp_33May/June 2026 · Paper 3 (Core)Q10
0580/43/M/J/260580_s26_qp_43May/June 2026 · Paper 4 (Extended)Q1
0580/12/F/M/260580_m26_qp_12Feb/Mar 2026 · Paper 1 (Core)Q3, Q4
0580/32/F/M/260580_m26_qp_32Feb/Mar 2026 · Paper 3 (Core)Q8
0580/11/O/N/250580_w25_qp_11Oct/Nov 2025 · Paper 1 (Core)Q20
0580/12/O/N/250580_w25_qp_12Oct/Nov 2025 · Paper 1 (Core)Q6
0580/21/O/N/250580_w25_qp_21Oct/Nov 2025 · Paper 2 (Extended)Q11
0580/23/O/N/250580_w25_qp_23Oct/Nov 2025 · Paper 2 (Extended)Q20
0580/31/O/N/250580_w25_qp_31Oct/Nov 2025 · Paper 3 (Core)Q4
0580/33/O/N/250580_w25_qp_33Oct/Nov 2025 · Paper 3 (Core)Q3
0580/11/M/J/250580_s25_qp_11May/June 2025 · Paper 1 (Core)Q8, Q24
0580/12/M/J/250580_s25_qp_12May/June 2025 · Paper 1 (Core)Q2, Q6, Q21
0580/13/M/J/250580_s25_qp_13May/June 2025 · Paper 1 (Core)Q1, Q24
0580/21/M/J/250580_s25_qp_21May/June 2025 · Paper 2 (Extended)Q4, Q7
0580/22/M/J/250580_s25_qp_22May/June 2025 · Paper 2 (Extended)Q14

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