IGCSE · Practice questions · Fractions, decimals and percentages

Divide, then times 100.

Six original Cambridge-style questions on fractions, decimals and percentages, including simplest form and (Extended) recurring decimals.

Original questions All questions on this page are original work, written in the Cambridge IGCSE style. They are not from past papers. They test the same concepts and skills the syllabus rewards.

The method

Go through the decimal, then cancel.

Fraction to decimal: top \(\div\) bottom.
Decimal to percentage: \(\times 100\); percentage to decimal: \(\div 100\).
Decimal to fraction: place value (tenths, hundredths, ...), then cancel by the HCF.
Mixed to improper: whole \(\times\) bottom \(+\) top, over the same bottom.
Recurring (Extended): let \(x\) = the decimal, multiply by a power of 10 to line up the repeats, subtract.

Recall

[2 marks]

Write 0.65 as (a) a fraction in its simplest form (b) a percentage.

(a) \(\dfrac{65}{100} = \dfrac{13}{20}\) ✓
(b) 65% ✓

Recall

[2 marks]

(a) Write \(4\dfrac{5}{7}\) as an improper fraction. (b) Write \(\dfrac{29}{4}\) as a mixed number.

(a) \(\dfrac{4 \times 7 + 5}{7} = \dfrac{33}{7}\) ✓
(b) \(29 \div 4 = 7\) r 1, so \(7\dfrac{1}{4}\) ✓

Calculation

[2 marks]

Without a calculator, write \(\dfrac{7}{8}\) as (a) a decimal (b) a percentage.

(a) \(7 \div 8 = 0.875\) ✓
(b) \(0.875 \times 100 = 87.5\%\) ✓

Calculation

[2 marks]

(Extended) Write \(\dfrac{7}{12}\) as a recurring decimal, using dot notation.

\(7 \div 12 = 0.58333\dots\) ✓
Only the 3 repeats: \(0.58\dot{3}\) ✓

Proof

[3 marks]

(Extended) Show that \(0.3\dot{6} = \dfrac{11}{30}\).

Let \(x = 0.3666\dots\) ✓
\(100x = 36.666\dots\) and \(10x = 3.666\dots\) ✓
\(100x - 10x = 33\), so \(90x = 33\) ✓
\(x = \dfrac{33}{90} = \dfrac{11}{30}\) ✓

Analysis

[4 marks]

240 people chose their favourite colour. 0.35 of them chose red, \(\dfrac{3}{8}\) chose blue, 15% chose green and the rest chose yellow.

(a) How many chose yellow? (b) What fraction of the people chose yellow? Give your answer in its simplest form.

Red: \(0.35 \times 240 = 84\). Blue: \(\dfrac{3}{8} \times 240 = 90\). Green: \(0.15 \times 240 = 36\). ✓
(a) Yellow: \(240 - 84 - 90 - 36 = 30\) ✓
(b) \(\dfrac{30}{240} = \dfrac{1}{8}\) ✓

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.