Fractions: add, subtract, multiply and divide – Year 6 maths test answers to download as PDF

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1. Answer to Question 1 (3 marks)

   1. The highest common factor of 28 and 42 is 14: 28 ÷ 14 = 2 and 42 ÷ 14 = 3, giving \(\frac{2}{3}\). (1 mark)
   2. 4 × 5 = 20, so multiply the numerator by 5 as well: 3 × 5 = 15, giving \(\frac{15}{20}\). (1 mark)
   3. Use twentieths: \(\frac{7}{10}\) = \(\frac{14}{20}\) and \(\frac{3}{4}\) = \(\frac{15}{20}\). 15 > 14, so \(\frac{3}{4}\) is bigger. (1 mark)

2. Answer to Question 2 (4 marks)

   1. Change fifths to tenths: \(\frac{4}{10}\) + \(\frac{3}{10}\) = \(\frac{7}{10}\). (1 mark)
   2. The lowest common multiple of 8 and 3 is 24: \(\frac{21}{24}\) − \(\frac{8}{24}\) = \(\frac{13}{24}\). (1 mark)
   3. Add the wholes (3) and the fractions in twelfths: \(\frac{8}{12}\) + \(\frac{9}{12}\) = \(\frac{17}{12}\) = \(1\frac{5}{12}\). Total \(4\frac{5}{12}\). (1 mark)
   4. Use sixths: \(4\frac{1}{6}\) − \(1\frac{4}{6}\). Exchange a whole: \(3\frac{7}{6}\) − \(1\frac{4}{6}\) = \(2\frac{3}{6}\) = \(2\frac{1}{2}\). (1 mark)

3. Answer to Question 3 (4 marks)

   1. Multiply tops and bottoms: \(\frac{15}{45}\), which simplifies (÷15) to \(\frac{1}{3}\). (1 mark)
   2. One eighth of 72 is 9, so five eighths is 9 × 5 = 45. (1 mark)
   3. Dividing by 6 makes the pieces 6 times smaller: \(\frac{3}{24}\) = \(\frac{1}{8}\). (1 mark)
   4. \(2\frac{1}{4}\) = \(\frac{9}{4}\), and \(\frac{9}{4}\) × \(\frac{2}{3}\) = \(\frac{18}{12}\) = \(1\frac{1}{2}\). (1 mark)

4. Answer to Question 4 (4 marks)

   1. Write Sunday's share in eighths, \(\frac{2}{8}\), and add Saturday's \(\frac{3}{8}\): together \(\frac{5}{8}\) of the cake has gone. (1 mark)
   2. Take the eaten part from the whole cake, \(\frac{8}{8}\): 8 − 5 = 3 eighths remain, \(\frac{3}{8}\). (1 mark)
   3. One third of three eighths is one eighth (3 eighths shared into 3 equal parts), so the neighbour gets \(\frac{1}{8}\) of the whole cake. (2 marks)

5. Answer to Question 5 (5 marks)

   1. \(\frac{3}{8}+\frac{1}{4}=\frac{5}{8}\), so adults are \(1-\frac{5}{8}=\) \(\frac{3}{8}\). (1 mark)
   2. \(\frac{3}{8}\) of 240 = 30 × 3 = 90 children. (1 mark)
   3. Adults: 90. \(\frac{2}{5}\) of 90: 90 ÷ 5 = 18, 18 × 2 = 36 adults. (1 mark)
   4. Total money: 240 × £2.50 = £600. \(\frac{3}{5}\) of £600 = 120 × 3 = £360. (2 marks)

Total : 20 marks