Equivalent fractions and comparing fractions – Year 3 maths test answers to download as PDF

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1. Answer to Question 1 (4 marks)

   1. The denominator 2 is multiplied by 4 to make 8, so multiply the numerator by 4 too: 1 × 4 = 4. The answer is \(\frac{4}{8}\). (1 mark)
   2. The numerator 2 is doubled to make 4, so double the denominator: 3 × 2 = 6. The answer is \(\frac{4}{6}\). (1 mark)
   3. The numerator 6 is halved to make 3, so halve the denominator: 10 ÷ 2 = 5. The answer is \(\frac{3}{5}\). (1 mark)
   4. Divide the numerator and the denominator of \(\frac{2}{4}\) by the same number, 2: 2 ÷ 2 = 1 and 4 ÷ 2 = 2, giving \(\frac{1}{2}\). A diagram also shows 2 quarters covering half a bar. (1 mark)

2. Answer to Question 2 (4 marks)

   1. Both fractions are sevenths, so compare the numerators: 3 is less than 5. So \(\frac{3}{7} \lt \frac{5}{7}\). (1 mark)
   2. Both are unit fractions. A whole cut into 4 parts has bigger parts than one cut into 8, so \(\frac{1}{4} \gt \frac{1}{8}\). (1 mark)
   3. Double the numerator and denominator of \(\frac{3}{4}\): \(\frac{6}{8}\). They are equivalent, so \(\frac{3}{4} = \frac{6}{8}\). (1 mark)
   4. For unit fractions, more parts means smaller parts. 6 is the biggest denominator, so the order is \(\frac{1}{6}, \frac{1}{3}, \frac{1}{2}\). (1 mark)

3. Answer to Question 3 (4 marks)

   1. The denominators are the same, so add the numerators: 2 + 5 = 7. \(\frac{2}{9} + \frac{5}{9} = \frac{7}{9}\). (1 mark)
   2. Subtract the numerators and keep the tenths: 7 − 4 = 3, so the answer is \(\frac{3}{10}\). (1 mark)
   3. 3 + 5 = 8, so the total is \(\frac{8}{8}\). Eight eighths make 1 whole. (1 mark)
   4. Ali and Bea eat 3 + 2 = 5 of the 8 pieces. 8 − 5 = 3 pieces are left, which is \(\frac{3}{8}\) of the bar. (1 mark)

4. Answer to Question 4 (4 marks)

   1. Each mark is one eighth. Count three marks from 0: one eighth, two eighths, three eighths. The fraction is \(\frac{3}{8}\). (1 mark)
   2. Half of 8 parts is 4 parts, so the 4th mark is \(\frac{4}{8}\), which is equivalent to \(\frac{1}{2}\). (1 mark)
   3. A quarter is 2 eighths, so three quarters is 6 eighths. The 6th mark, \(\frac{6}{8}\), is equivalent to \(\frac{3}{4}\). (1 mark)
   4. The line from 0 to 1 is cut into 8 equal parts, so 8 eighths make one whole: \(\frac{8}{8} = 1\). (1 mark)

5. Answer to Question 5 (4 marks)

   1. Kim eats 4 of the 12 slices: \(\frac{4}{12}\). Divide the numerator and denominator by 4: \(\frac{4}{12} = \frac{1}{3}\). (2 marks: 1 for \(\frac{4}{12}\), 1 for simplest form)
   2. Add the slices eaten: 3 + 4 + 2 = 9, so \(\frac{9}{12}\) is eaten. Dividing both numbers by 3 gives \(\frac{3}{4}\). (1 mark)
   3. 12 − 9 = 3 slices are left: \(\frac{3}{12}\), which simplifies to \(\frac{1}{4}\). Check: \(\frac{3}{4} + \frac{1}{4} = 1\) whole pie. (1 mark)

Total : 20 marks