Worksheets · Foundation and Higher

Fraction arithmetic and exact answers

3 exam-style questions. Answers and the mark for each step are on the last page.

Question 1Non-calculator · 4 marks
Answer each part without a calculator.
(a) Work out $\frac{3}{8}$ of $64$ . (2)
(b) A circle has an area of $25\pi\ \text{cm}^2$ . A sector is $\frac{2}{5}$ of the circle. Work out the area of the sector. Give your answer in terms of $\pi$ . (2)
Question 2Non-calculator · 5 marks
A charity has 72 badges. It sells one quarter in the morning, then two thirds of the remaining badges in the afternoon.
(a) How many badges remain unsold? (3)
(b) What fraction of the original badges was sold altogether? (2)
Question 3Non-calculator · 5 marks
A water tank is $\frac{3}{5}$ full. After $42$ litres are used, the tank is $\frac{1}{4}$ full.
(a) Work out the capacity of the tank, in litres. (3)
(b) Next, $\frac{2}{3}$ of the water left in the tank is used. What fraction of the tank is now full? (2)

Answers and marks

(a) $24$

(b) $10\pi\ \text{cm}^2$

(a) $18$

(b) $\frac{3}{4}$

(a) $120$ litres

P1 Finding the fraction used, $\frac{7}{20}$ .
P1 Setting $\frac{7}{20}$ of the capacity equal to 42, or finding $\frac{1}{20} = 6$ .
A1 The correct answer, $120$ litres.

(b) $\frac{1}{12}$

M1 Finding $\frac{1}{3}$ of $\frac{1}{4}$ , or finding the $30 - 20 = 10$ litres left out of $120$ .
A1 The correct answer, $\frac{1}{12}$ .

Fraction arithmetic and exact answers

Type your working online and see every mark you earned and lost.