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4MA1/1F Jun 2019, Question 9: Mixed Numbers and Improper Fractions

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1F (Foundation) · Calculator · 7 marks

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The question, in short

Order four fractions by size starting with the smallest, then show two fraction calculations give the stated results.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 2 marks

Arrange 7/10, 4/5, 1/2 and 29/40 from smallest to largest.

  1. 1Write each fraction over 40
  2. 27/10 = 28/40, 4/5 = 32/40, 1/2 = 20/40, 29/40 stays
  3. 3Order: 20/40, 28/40, 29/40, 32/40, so 1/2, 7/10, 29/40, 4/5

Answer1/2, 7/10, 29/40, 4/5

Part (b) · 2 marks

Show that adding 8/15 and 3/10 gives 5/6.

  1. 1The lowest common multiple of 15 and 10 is 30
  2. 28/15 = 16/30 and 3/10 = 9/30
  3. 316/30 + 9/30 = 25/30
  4. 4Divide numerator and denominator by 5: 25/30 = 5/6
  5. 5So 8/15 + 3/10 = 5/6

Answer8/15 + 3/10 = 16/30 + 9/30 = 25/30 = 5/6

Part (c) · 3 marks

Show that dividing 4 2/3 by 1 1/9 gives 4 1/5.

  1. 1Write both mixed numbers as improper fractions
  2. 24 2/3 = 14/3 and 1 1/9 = 10/9
  3. 3To divide, multiply by the reciprocal: 14/3 ÷ 10/9 = 14/3 × 9/10
  4. 414/3 × 9/10 = 126/30
  5. 5Divide numerator and denominator by 6: 126/30 = 21/5
  6. 621/5 = 4 1/5, so 4 2/3 ÷ 1 1/9 = 4 1/5

Answer14/3 ÷ 10/9 = 14/3 × 9/10 = 126/30 = 21/5 = 4 1/5

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