NavGanitMateby NavGreen Compute, AustraliaBased on Victorian Curriculum Mathematics v2.0
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Rates and unit comparisons

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A school in Canberra is ordering art supplies for 8 classes. The order includes 72 tubes of paint and 35 sets of brushes.

Each class is to receive the same number of paint tubes and the same number of brush sets.

What is the exact rate of paint tubes per class, expressed as a simplified fraction?

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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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Worked solution and answer (click to reveal)

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Worked solution

  1. The school is ordering 72 tubes of paint for 8 classes. We need to find how many paint tubes each class receives.
  2. The rate of paint tubes per class is calculated by dividing the total number of paint tubes by the number of classes.
  3. Substitute the given values: 72 tubes ÷ 8 classes.
  4. Perform the division: 72 ÷ 8 = 9.
  5. The result is 9 tubes per class, which is a whole number.
  6. Express the rate as a fraction: 72/8.
  7. Simplify the fraction 72/8 by dividing both numerator and denominator by their greatest common divisor, which is 8.
  8. 72 ÷ 8 = 9, and 8 ÷ 8 = 1. So, 72/8 = 9/1.
  9. The simplified fraction is 9/1.
  10. Check: 9/1 × 8 = 72, which matches the total number of paint tubes.
  11. The rate of paint tubes per class is exactly 9/1.
  12. The answer is 9/1, which is the simplified fraction form of the rate.

Reference answer: 9/1

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