Maths worksheets · lesson 43 of 64 · free

Ratio, proportion and the unitary method — Maths worksheet

A ratio compares two quantities of the same kind: 12 boys and 18 girls are in the ratio 12 : 18, which is 2 : 3 in its simplest form. Four numbers are in proportion when their two ratios are equal. The unitary method answers "if 5 pens cost ₹60, what do 8 cost?" — first find the cost of one pen.

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The method

Find one first — “unitary method: find the value of one thing, then multiply”

  1. Simplest form: divide both terms by their HCF — 12 : 18 = 2 : 3.
  2. Equal ratios: multiply (or divide) both terms by the same number — 3 : 4 = 15 : 20.
  3. a, b, c, d are in proportion when a × d = b × c.
  4. Unitary method: value of one = total ÷ number; then × the number you need. To share in a ratio 2 : 3, split into 2 + 3 = 5 equal parts.

Use it for: Prices in shops, recipes for more people, speed and distance, sharing pocket money, and the ratio and proportion chapter of Class 6 maths.

🧮 Check your own sums with the free Ratio calculator — it shows the working.

Worked example: If 5 pens cost ₹60, how many rupees do 8 pens cost? → 96

  1. Unitary method: 1 pen costs ₹60 ÷ 5 = ₹12.
  2. 12 × 8 = 96.

Check: 5 pens : 8 pens = 60 : 96, and 5 × 96 = 480 = 8 × 60 ✓

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🏁 Lesson 43 test

20 sums. Check each answer, then go to the next one. Get 16 or more right to pass.

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🖨️ Class 6 Maths Worksheet: Ratio and Proportion

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