NavGanitMateby NavGreen Compute, AustraliaBased on Victorian Curriculum Mathematics v2.0
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Calculating with rational numbers

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Required skills (click to reveal)

A craft designer in Brisbane is creating a geometric pattern using strips of coloured fabric. Each strip is 18/25 metres long.

The designer needs to join 87 such strips end-to-end to form a continuous ribbon. What is the exact total length, in metres, of the ribbon?

Express your answer as a single exact fraction.

Concept illustrations

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Two red counters for every three blue counters. Red:blue = 2:3. There are 5 counters in all, so the red fraction of the whole is 2/5.RedRedBlueBlueBlue2 red : 3 blue · 5 counters in all
Red:blue = 2:3. There are 5 counters in all, so the red fraction of the whole is 2/5.
Translate a situation into a model. With a fixed charge of $4 and $2 per kilometre, cost C = 4 + 2d. At d = 3 km the cost is $10. Assume this tariff applies for the trip.$4 + $2/kmDefine tariff→C = 4 + 2dBuild rule→d=3 → C=$10Interpret
With a fixed charge of $4 and $2 per kilometre, cost C = 4 + 2d. At d = 3 km the cost is $10. Assume this tariff applies for the trip.

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Formula

Explanation

Worked solution and answer (click to reveal)

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Worked solution

  1. The length of each fabric strip is given as 18/25 metres.
  2. The designer needs to join 87 such strips end-to-end.
  3. To find the total length, multiply the length of one strip by the number of strips: total length = 87 × (18/25) metres.
  4. First, write 87 as a fraction: 87/1.
  5. Multiply the two fractions: (87/1) × (18/25) = (87 × 18) / (1 × 25).
  6. Calculate 87 × 18: 87 × 18 = (80 + 7) × 18 = 80×18 + 7×18 = 1440 + 126 = 1566.
  7. Now the fraction is 1566 / 25.
  8. Check if the fraction can be simplified. Find the greatest common divisor (GCD) of 1566 and 25.
  9. 25 factors as 5². Check if 5 divides 1566: 1566 ÷ 5 = 313.2, not an integer. So 5 does not divide 1566. Therefore, GCD is 1.
  10. The fraction 1566/25 is already in simplest form.
  11. The total length of the ribbon is 1566/25 metres.
  12. This is the exact total length, expressed as a single fraction.

Reference answer: 1566/25

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