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0580/42 May/Jun 2022, Question 1: Dividing in a Given Ratio

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 10 marks

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The question, in short

Five unrelated calculations: find an LCM, divide money in a three-part ratio, evaluate a division of numbers in standard form, convert a recurring decimal to a fraction, and calculate a density with units.

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

Part (a) · 2 marks

Determine the smallest number that is a multiple of both 30 and 75.

  1. 130 = 2 × 3 × 5, 75 = 3 × 5²
  2. 2LCM = 2 × 3 × 5² = 150

Answer150

Part (b) · 3 marks

Split $608 into three amounts proportional to 4, 5 and 7.

  1. 14 + 5 + 7 = 16 parts, 1 part = 608 ÷ 16 = 38
  2. 24 × 38 = 152, 5 × 38 = 190, 7 × 38 = 266
  3. 3$152, $190, $266

Answer152, 190, 266

Part (c) · 2 marks

Compute (6.39 × 10⁴) ÷ (2.45 × 10⁶) and express the result in standard form.

  1. 1(6.39 ÷ 2.45) × 10⁴⁻⁶ = 2.608… × 10⁻²
  2. 2≈ 2.61 × 10⁻²

Answer2.61 × 10⁻² or 2.608… × 10⁻²

Part (d) · 1 mark

Express the recurring decimal 0.2̇7̇ as a fraction.

  1. 1x = 0.2727…, 100x = 27.2727…
  2. 299x = 27
  3. 3x = 27/99

Answer27/99

Part (e) · 2 marks

For a stone of volume 45 cm³ and mass 126 g, work out its density using mass ÷ volume, stating the units.

  1. 1Density = 126 ÷ 45
  2. 2= 2.8 g/cm³

Answer2.8 g/cm³ or 2.8 g cm⁻³

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