Adding, subtracting and multiplying fractions – Year 5 maths test answers to download as PDF

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1. Answer to Question 1 (4 marks)

   (a) The denominators are the same, so add the numerators: 2 + 5 = 7 ninths, \(\frac{7}{9}\). (1 mark)

   (b) Same denominators again: 7 − 3 = 4 eighths, \(\frac{4}{8}\), which simplifies to \(\frac{1}{2}\). (1 mark)

   (c) Change quarters to eighths: \(\frac{3}{4}\) = \(\frac{6}{8}\). Then \(\frac{6}{8}\) + \(\frac{5}{8}\) = \(\frac{11}{8}\) = \(1\frac{3}{8}\). (1 mark)

   (d) Change thirds to sixths: \(\frac{1}{3}\) = \(\frac{2}{6}\). Then \(\frac{5}{6}\) − \(\frac{2}{6}\) = \(\frac{3}{6}\) = \(\frac{1}{2}\). (1 mark)

2. Answer to Question 2 (4 marks)

   (a) Whole numbers: 2 + 1 = 3. Fractions: \(\frac{1}{3}\) + \(\frac{1}{3}\) = \(\frac{2}{3}\). Answer: \(3\frac{2}{3}\). (1 mark)

   (b) 3 + 1 = 4 and \(\frac{3}{4}\) + \(\frac{2}{4}\) = \(\frac{5}{4}\) = \(1\frac{1}{4}\). Answer: \(5\frac{1}{4}\). (1 mark)

   (c) \(4\frac{2}{4}\) − \(1\frac{3}{4}\) = \(3\frac{6}{4}\) − \(1\frac{3}{4}\) = \(2\frac{3}{4}\). (1 mark)

   (d) 5 = \(4\frac{5}{5}\). \(4\frac{5}{5}\) − \(2\frac{2}{5}\) = \(2\frac{3}{5}\). (1 mark)

3. Answer to Question 3 (4 marks)

   (a) Multiply the numerator by 4: 4 × 2 = 8, giving \(\frac{8}{5}\) = \(1\frac{3}{5}\). (1 mark)

   (b) 6 × 3 = 18 quarters, \(\frac{18}{4}\), which is 4 wholes and 2 quarters: \(4\frac{1}{2}\). (1 mark)

   (c) Multiply the whole and the fraction separately: 3 × 2 = 6 and 3 × \(\frac{1}{3}\) = 1, so 6 + 1 = 7. (1 mark)

   (d) Find one fifth first: 40 ÷ 5 = 8. Three fifths is 8 × 3 = 24. (1 mark)

4. Answer to Question 4 (3 marks)

   (a) Ben added the denominators. The size of the pieces (fifths) does not change. (1 mark)

   (b) \(\frac{3}{5}\). (1 mark)

   (c) \(\frac{1}{2}\) = \(\frac{2}{4}\), and \(\frac{2}{4}\) + \(\frac{1}{4}\) = \(\frac{3}{4}\), which is more than \(\frac{1}{2}\). But \(\frac{2}{6}\) = \(\frac{1}{3}\) is less than \(\frac{1}{2}\), so it cannot be right. The correct answer is \(\frac{3}{4}\). (1 mark)

5. Answer to Question 5 (5 marks)

   (a) Whole numbers: 6 + 7 + 5 = 18. Fractions: \(\frac{2}{4}\) + \(\frac{1}{4}\) + \(\frac{3}{4}\) = \(\frac{6}{4}\) = \(1\frac{1}{2}\). Total = \(19\frac{1}{2}\) miles. (2 marks)

   (b) 26 − \(19\frac{1}{2}\) = \(6\frac{1}{2}\) miles. (1 mark)

   (c) 4 × \(\frac{13}{2}\) = \(\frac{52}{2}\) = 26 miles. (1 mark)

   (d) It is exactly 26 miles, so the difference is 0 miles: it is the same distance. (1 mark)

Total : 20 marks