Fractions: equivalent, mixed numbers and improper – Year 5 maths test answers to download as PDF

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1. Answer to Question 1 (4 marks)

   (a) 6 × 4 = 24, so 5 × 4 = 20. (1 mark)

   (b) Divide by 6: \(\frac{3}{5}\). (1 mark)

   (c) For example \(\frac{4}{10}\), \(\frac{6}{15}\), \(\frac{8}{20}\). (1 mark)

   (d) \(\frac{3}{4}\) = \(\frac{12}{16}\), which is not \(\frac{9}{16}\), so no. (1 mark)

2. Answer to Question 2 (4 marks)

   (a) 23 ÷ 5 = 4 remainder 3, so \(4\frac{3}{5}\). (1 mark)

   (b) 4 × 3 + 2 = 14, so \(\frac{14}{3}\). (1 mark)

   (c) 15 ÷ 4 = 3 remainder 3, so \(3\frac{3}{4}\). (1 mark)

   (d) 2 × 8 + 5 = 21, so \(\frac{21}{8}\). (1 mark)

3. Answer to Question 3 (4 marks)

   (a) Change to eighths: \(\frac{3}{4}\) = \(\frac{6}{8}\). 5 eighths is less than 6 eighths, so \(\frac{5}{8}\) < \(\frac{3}{4}\). (1 mark)

   (b) Use twelfths: \(\frac{2}{3}\) = \(\frac{8}{12}\) and \(\frac{5}{6}\) = \(\frac{10}{12}\). Comparing 7, 8 and 10 twelfths gives \(\frac{7}{12}\), \(\frac{2}{3}\), \(\frac{5}{6}\). (2 marks)

   (c) Use sixths: \(2\frac{1}{2}\) = \(\frac{15}{6}\) and \(\frac{7}{3}\) = \(\frac{14}{6}\). Since 15 > 14, \(2\frac{1}{2}\) is bigger. (1 mark)

4. Answer to Question 4 (3 marks)

   (a) 5 halves make 2 wholes (4 halves) and 1 half left over: \(2\frac{1}{2}\). (1 mark)

   (b) 11 ÷ 4 = 2 remainder 3, so \(\frac{11}{4}\) = \(2\frac{3}{4}\). It lies between 2 and 3. (1 mark)

   (c) Any number bigger than one and a half but smaller than 2 works, for example \(1\frac{3}{4}\) (which is \(\frac{7}{4}\)). (1 mark)

5. Answer to Question 5 (5 marks)

   (a) 13 ÷ 8 = 1 remainder 5, so \(1\frac{5}{8}\). (1 mark)

   (b) Zoe \(\frac{13}{8}\); Omar \(\frac{7}{4}\) = \(\frac{14}{8}\); Pia \(1\frac{1}{2}\) = \(\frac{12}{8}\). Total: 13 + 14 + 12 = 39 eighths = \(\frac{39}{8}\). (2 marks)

   (c) 6 sandwiches = \(\frac{48}{8}\). Sam eats 48 − 39 = 9 eighths = \(1\frac{1}{8}\) sandwiches. (1 mark)

   (d) Omar eats \(\frac{14}{8}\), the most, so Omar. (1 mark)

Total : 20 marks