IGCSE · Practice questions · The four operations: fractions, negatives and order of operations

BIDMAS, signs, reciprocals.

Six original Cambridge-style questions on the four operations with integers, negatives, fractions, mixed numbers and 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

Order, signs, then the fraction rules.

Order: brackets, indices, \(\times \div\) left to right, \(+ -\) left to right.
Signs: subtracting a negative adds; same signs multiply or divide to a positive.
Mixed numbers: make them improper first.
Add/subtract fractions: common denominator. Divide: multiply by the reciprocal.
Decimals: count decimal places to multiply; scale both numbers to divide by a whole number.

Recall

[2 marks]

Work out (a) \(7 - (-5)\) (b) \((-3) \times 4 \times (-2)\).

(a) \(7 + 5 = 12\) ✓
(b) \(-12 \times -2 = 24\) ✓

Calculation

[2 marks]

Without a calculator, work out \(2\dfrac{2}{5} + 1\dfrac{3}{4}\). Give your answer as a mixed number.

\(\dfrac{12}{5} + \dfrac{7}{4} = \dfrac{48}{20} + \dfrac{35}{20} = \dfrac{83}{20}\) ✓
\(= 4\dfrac{3}{20}\) ✓

Calculation

[3 marks]

Without a calculator, work out \(3\dfrac{1}{3} \div 1\dfrac{7}{9}\). Give your answer as a mixed number in its simplest form.

\(\dfrac{10}{3} \div \dfrac{16}{9} = \dfrac{10}{3} \times \dfrac{9}{16}\) ✓
\(= \dfrac{90}{48} = \dfrac{15}{8}\) ✓
\(= 1\dfrac{7}{8}\) ✓

Analysis

[2 marks]

Insert two pairs of brackets to make this statement true: \(\ 3 + 5 \times 6 - 2 = 32\)

\((3 + 5) \times (6 - 2) = 8 \times 4 = 32\) ✓

Calculation

[2 marks]

Without a calculator, work out (a) \(0.36 \div 0.004\) (b) \(2.5 \times 0.12\).

(a) Multiply both by 1000: \(360 \div 4 = 90\) ✓
(b) \(25 \times 12 = 300\); 3 decimal places gives \(0.300 = 0.3\) ✓

Analysis

[4 marks]

A water tank holds 240 litres when full. It is \(\dfrac{5}{6}\) full. Sam uses \(\dfrac{2}{5}\) of the water in the tank, and then 35 litres are added.

(a) How many litres are now in the tank? (b) What fraction of the tank is now full? Give your answer in its simplest form.

Water at the start: \(\dfrac{5}{6} \times 240 = 200\) litres. ✓
Sam uses \(\dfrac{2}{5} \times 200 = 80\) litres, leaving 120 litres. ✓
(a) \(120 + 35 = 155\) litres ✓
(b) \(\dfrac{155}{240} = \dfrac{31}{48}\) ✓

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.