Elite Mathematics / Linear / Topics / Fractions IGCSE · 4MA1 · Topic Fractions: past paper questions & worked solutions
Every Fractions question from the 4MA1 papers in our bank, 2020–2026, sorted from easiest to hardest. Try each one first, then open the worked solution.
18 questions
54 marks in total
33% of papers (18 of 54) include it
1/17/0 easy / medium / hard
Questions, easiest first Level is estimated from marks: 1–2 easy, 3–4 medium, 5+ hard.
1. Jun 2026 P2HR · Q17 Easy 2 marksShow worked solution Solution | Step 1 Let \(z=0.\overline{814}=0.814814814\ldots\). Then \(1000z=814.814814\ldots\).
Multiplication by 1000 aligns the repeating three-digit tails.
Solution | Step 2 \[1000z-z=814\quad\Rightarrow\quad999z=814\quad\Rightarrow\quad z=\frac{814}{999}=\frac{22}{27}.\]
Subtract to cancel the recurring tails, then cancel the common factor 37.
Final answer \(0.\overline{814}=\frac{22}{27}\).
2. Jun 2026 P1H · Q1 Medium 3 marksShow worked solution Solution | Step 1 \[4\frac17=\frac{29}{7},\qquad 2\frac35=\frac{13}{5}.\]
Convert each mixed number to an improper fraction.
Solution | Step 2 \[\frac{29}{7}-\frac{13}{5}=\frac{145-91}{35}=\frac{54}{35}=1\frac{19}{35}.\]
Use the common denominator 35, subtract, then convert back to a mixed number.
Final answer \(1\frac{19}{35}\)
3. Jun 2026 P1HR · Q1 Medium 3 marksShow worked solution Solution | Step 1 \[2\frac45=\frac{14}{5},\qquad 3\frac37=\frac{24}{7}.\]
Convert each mixed number into an improper fraction.
Solution | Step 2 \[\frac{14}{5}\times\frac{24}{7}=\frac{2\times24}{5}=\frac{48}{5}=9\frac35.\]
Cancel the common factor 7, multiply, then convert back to a mixed number.
Final answer \(2\frac45\times3\frac37=9\frac35\)
4. May 2026 4WM1H · Q1 Medium 3 marksShow worked solution Improper fractions \[4\tfrac17=\frac{29}{7},\qquad 2\tfrac35=\frac{13}{5}\]
Common denominator 35 \[\frac{29}{7}-\frac{13}{5}=\frac{145}{35}-\frac{91}{35}=\frac{54}{35}\]
Back to a mixed number \[\frac{54}{35}=1\tfrac{19}{35}\quad\text{as required.}\]
Final answer \(\frac{54}{35}=1\frac{19}{35}\) (shown)
5. Nov 2025 4WM1H · Q3 Medium 3 marksShow worked solution Evaluate fraction \[
\frac37+\frac13
\]
Use denominator 21 Use denominator 21: \[ \frac37=\frac9{21},\qquad \frac13=\frac7{21} \]
\[
\frac9{21}+\frac7{21}=\frac{16}{21}
\]
Final answer \(\frac{16}{21}\).
6. May 2025 4WM1H · Q1 Medium 3 marksShow worked solution Simplify fraction Convert the mixed numbers to improper fractions.
\[
3\frac{2}{3}=\frac{11}{3},\qquad 2\frac{4}{7}=\frac{18}{7}
\]
Simplify fraction Then multiply.
\[
\frac{11}{3}\times\frac{18}{7}=\frac{198}{21}=\frac{66}{7}
\]
Convert to a mixed number Convert to a mixed number.
\[
\frac{66}{7}=9\frac{3}{7}
\]
Final answer \(9\frac{3}{7}\)
7. May 2025 4WM1HR · Q2 Medium 3 marksShow worked solution Evaluate fraction \[
2\frac14=\frac94,\qquad 1\frac57=\frac{12}{7}
\]
\[
2\frac14\times1\frac57=\frac94\times\frac{12}{7}
\]
\[
=\frac{108}{28}=\frac{27}{7}=3\frac67
\]
Final answer \(3\frac67\).
8. Jun 2024 P2H · Q4 Medium 3 marksShow worked solution Simplify fraction \[
2\frac47=\frac{18}{7}
\]
\[
3\frac19=\frac{28}{9}
\]
Simplify fraction Now multiply:
\[
\frac{18}{7}\times \frac{28}{9}
\]
Cancel first Cancel first:
\[
\frac{18}{9}\times \frac{28}{7}=2\times 4=8
\]
9. Jun 2022 P2H · Q4 Medium 3 marksShow worked solution Simplify fraction \[
5\frac13=\frac{16}{3}
\]
\[
2\frac67=\frac{20}{7}
\]
Use a common denominator Use a common denominator:
\[
\frac{16}{3}-\frac{20}{7}
=\frac{112}{21}-\frac{60}{21}
\]
\[
=\frac{52}{21}=2\frac{10}{21}
\]
Final answer \(2\frac{10}{21}\)
10. Jun 2022 P1HR · Q6 Medium 3 marksShow worked solution Simplify fraction \[
2\frac23=\frac83
\]
\[
3\frac34=\frac{15}{4}
\]
Use a common denominator Use a common denominator:
\[
\frac83+\frac{15}{4}
=\frac{32}{12}+\frac{45}{12}
\]
\[
=\frac{77}{12}=6\frac5{12}
\]
Final answer \(6\frac5{12}\)
11. Jan 2022 P2H · Q2 Medium 3 marksShow worked solution Convert to improper fractions Convert to improper fractions:
\[
6\frac34=\frac{27}{4}
\]
\[
2\frac47=\frac{18}{7}
\]
Divide by multiplying by the Divide by multiplying by the reciprocal:
\[
\frac{27}{4}\div \frac{18}{7}
=\frac{27}{4}\times \frac{7}{18}
\]
\[
=\frac{21}{8}=2\frac58
\]
12. May 2021 P2H · Q2 Medium 3 marksShow worked solution Simplify fraction \[
2\frac47=\frac{18}{7}
\]
\[
1\frac18=\frac98
\]
Divide by multiplying by the Divide by multiplying by the reciprocal:
\[
\frac{18}{7}\div \frac98
=\frac{18}{7}\times \frac89
\]
\[
=\frac{16}{7}=2\frac27
\]
13. Jan 2021 P1HR · Q1 Medium 3 marksShow worked solution Simplify fraction Convert the mixed numbers to improper fractions:
\[
3\frac15=\frac{16}{5}
\]
\[
1\frac56=\frac{11}{6}
\]
Simplify fraction Now multiply:
\[
\frac{16}{5}\times \frac{11}{6}
=\frac{176}{30}
\]
\[
=\frac{88}{15}=5\frac{13}{15}
\]
Final answer \(5\frac{13}{15}\)
14. Jan 2020 P1HR · Q2 Medium 3 marksShow worked solution Simplify fraction Convert the mixed numbers to improper fractions:
\[
3\frac15=\frac{16}{5}
\]
\[
2\frac58=\frac{21}{8}
\]
Simplify fraction Now multiply:
\[
\frac{16}{5}\times \frac{21}{8}
=\frac{2\times 21}{5}
\]
\[
=\frac{42}{5}=8\frac25
\]
15. Jan 2020 P2H · Q3 Medium 3 marksShow worked solution Convert to improper fractions Convert to improper fractions:
\[
4\frac23=\frac{14}{3}
\]
\[
3\frac45=\frac{19}{5}
\]
Use a common denominator Use a common denominator:
\[
\frac{14}{3}+\frac{19}{5}
=\frac{70}{15}+\frac{57}{15}
\]
\[
=\frac{127}{15}=8\frac{7}{15}
\]
Final answer \(8\frac{7}{15}\)
16. May-Nov 2020 P1HR · Q1 Medium 3 marksShow worked solution Simplify fraction \[
3\frac34=\frac{15}{4}
\]
Simplify fraction Now multiply:
\[
\frac{15}{4}\times \frac79
\]
Simplify fraction Cancel \(15\) and \(9\):
\[
\frac{5}{4}\times \frac73=\frac{35}{12}
\]
\[
\frac{35}{12}=2\frac{11}{12}
\]
Final answer \(2\frac{11}{12}\)
17. Specimen 4WM1H · Q2 Medium 3 marksShow worked solution Convert to improper fractions \[
5\frac13=\frac{16}{3},\qquad 2\frac67=\frac{20}{7}
\]
Use a common denominator \[
\frac{16}{3}-\frac{20}{7}
=\frac{112}{21}-\frac{60}{21}
=\frac{52}{21}
\]
Convert back to a mixed number \[
\frac{52}{21}=2\frac{10}{21}
\]
Final answer \(2\frac{10}{21}\).
18. Nov 2025 P2H · Q3 Medium 4 marksShow worked solution There are red and blue There are \(9+43=52\) red and blue bricks.
Simplify fraction Let the total number of bricks be \(T\).
Simplify fraction Since \(\frac7{20}\) of the bricks are yellow, the remaining fraction is
\[
1-\frac7{20}=\frac{13}{20}
\]
Simplify fraction So
\[
\frac{13}{20}T=52
\]
\[
T=52\times \frac{20}{13}=80
\]
Yellow bricks Yellow bricks:
\[
\frac7{20}\times 80=28
\]
Simplify fraction Each brick weighs \(35\) grams, so total yellow-brick weight is
\[
28\times 35=980
\]
Final answer \(980\) grams
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