Elite Mathematics / Linear / Topics / Fractions, Decimals and Percentages IGCSE · 4MA1 · Topic Fractions, Decimals and Percentages: past paper questions & worked solutions
Every Fractions, Decimals and Percentages question from the 4MA1 papers in our bank, 2021–2025, plus original Elite practice questions, sorted from easiest to hardest. Try each one first, then open the worked solution.
11 questions
25 marks in total
7% of papers (4 of 54) include it
8/3/0 easy / medium / hard
Questions, easiest first Level is estimated from marks: 1–2 easy, 3–4 medium, 5+ hard.
1. Jun 2025 P1HR · Q16 Easy 2 marksShow worked solution Let \[
x=0.6121212\ldots
\]
Calculate value Then \[ 10x=6.121212\ldots \]
Calculate value and \[ 1000x=612.121212\ldots \]
Subtract Subtract: \[ 1000x-10x=612.121212\ldots-6.121212\ldots \]
\[
990x=606
\]
\[
x=\frac{606}{990}=\frac{101}{165}
\]
Final answer \(0.6121212\ldots=\dfrac{101}{165}\).
2. May 2025 4WM1HR · Q14 Easy 2 marksShow worked solution Let \[
x=0.6121212\ldots
\]
Calculate value Then \[ 10x=6.121212\ldots \]
Calculate value and \[ 1000x=612.121212\ldots \]
Subtract Subtract: \[ 1000x-10x=612.121212\ldots-6.121212\ldots \]
\[
990x=606
\]
\[
x=\frac{606}{990}=\frac{101}{165}
\]
Final answer \(0.6121212\ldots=\dfrac{101}{165}\).
3. May 2021 P1H · Q16 Easy 2 marksShow worked solution Let \[
x=0.28131313\ldots
\]
Calculate value Then \[ 100x=28.131313\ldots \]
Calculate value and \[ 10000x=2813.131313\ldots \]
Subtract Subtract: \[ 10000x-100x=2813.131313\ldots-28.131313\ldots \]
\[
9900x=2785
\]
\[
x=\frac{2785}{9900}=\frac{557}{1980}
\]
Final answer \(0.28131313\ldots=\dfrac{557}{1980}\).
4. Elite Practice · Q15 Easy 2 marksShow worked solution Change every number to a decimal \(0.62\), \(\frac58=0.625\), \(61\%=0.61\), \(\frac23=0.666\ldots\), \(\frac35=0.6\)
Order them \(0.6,\ 0.61,\ 0.62,\ 0.625,\ 0.666\ldots\)
Final answer \(\frac35,\ 61\%,\ 0.62,\ \frac58,\ \frac23\)
5. Elite Practice · Q16 Easy 2 marksShow worked solution (a) Divide \[
7\div40=0.175
\]
(b) Multiply by 100 \[
0.175\times100=17.5\%
\]
Final answer (a) \(0.175\) (b) \(17.5\%\)
6. Elite Practice · Q18 Easy 2 marksShow worked solution Write both as decimals \[
\frac{13}{20}=13\div20=0.65
\]
Compare \(0.66>0.65\), so \(0.66\) is larger.
7. Elite Practice · Q19 Easy 2 marksShow worked solution Change the first score to a percentage \[
\frac{34}{40}\times100=85\%
\]
Compare \(87\%>85\%\), so the second test was better.
Final answer The second test (\(85\%\) against \(87\%\))
8. Elite Practice · Q20 Easy 2 marksShow worked solution Write over a power of 10 \[
0.0375=\frac{375}{10\,000}
\]
Simplify (divide by 125) \[
\frac{375}{10\,000}=\frac{3}{80}
\]
Final answer \(\dfrac{3}{80}\)
9. Nov 2021 P1H · Q18 Medium 3 marksShow worked solution Let \[
y=0.4\dot{x}
\]
Simplify fraction So
\[
y=0.4xxx\ldots
\]
Simplify fraction Multiply by \(10\) and \(100\):
\[
10y=4.xxx\ldots
\]
\[
100y=4x.xxx\ldots
\]
Subtract Subtract:
\[
100y-10y=(4x.xxx\ldots)-(4.xxx\ldots)
\]
\[
90y=x+36
\]
Simplify fraction Therefore
\[
y=\frac{x+36}{90}
\]
Final answer \(\frac{x+36}{90}\)
10. Elite Practice · Q17 Medium 3 marksShow worked solution Proportion that walk or cycle \[
\frac38+0.35=0.375+0.35=0.725
\]
Proportion that travel by bus \[
1-0.725=0.275
\]
Number of students \[
0.275\times n=11 \;\Rightarrow\; n=\frac{11}{0.275}=40
\]
11. Elite Practice · Q21 Medium 3 marksShow worked solution Change both amounts to percentages \(\frac25=40\%\), so the \(120\) litres fill \(65\%-40\%=25\%\) of the tank.
Find 100% \[
25\%\to120 \;\Rightarrow\; 100\%\to120\times4=480\text{ litres}
\]
Final answer \(480\) litres
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