Worksheets · Foundation and Higher

Equivalent fractions and mixed numbers

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) Write $\frac{18}{24}$ in its simplest form. (1)
(b) Write $2\frac{3}{5}$ as an improper fraction. (1)
(c) Write $\frac{17}{4}$ as a mixed number. (1)
(d) Which is larger, $\frac{5}{8}$ or $0.6$ ? (1)
1. $\frac{5}{8}$
2. $0.6$
Question 2Non-calculator · 4 marks
A carpenter has planks of length $2\frac{3}{5}$ m.
(a) Write $2\frac{3}{5}$ as an improper fraction. (2)
(b) Four planks are laid end to end. Find the total length. Give your answer as a mixed number. (2)
Question 3Non-calculator · 5 marks
A unit fraction $\frac{1}{n}$ has a whole number $n$ as its denominator. Some unit fractions are terminating decimals, such as $\frac{1}{4} = 0.25$ ; others recur, such as $\frac{1}{3} = 0.333\ldots$
(a) For how many whole numbers $n$ from $2$ to $20$ is $\frac{1}{n}$ a terminating decimal? (2)
(b) Explain why $\frac{7}{35}$ is a terminating decimal, even though $35$ has a prime factor of $7$ . (1)
(c) Write $0.375$ as a fraction in its simplest form. (2)

Answers and marks

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

(b) $\frac{13}{5}$

(c) $4\frac{1}{4}$

(d) $\frac{5}{8}$

(a) $\frac{13}{5}$

(b) 10 2/5 m

(a) $7$

(b) $\frac{7}{35} = \frac{1}{5} = 0.2$

C1 Simplifying to $\frac{1}{5}$ (or $0.2$ ) and saying the simplified denominator has only the prime factor 5.

(c) $\frac{3}{8}$

Equivalent fractions and mixed numbers

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