Proportional Reasoning

Proportional Reasoning

Process of solving a problem using mathematical reasoning that involve ratios or a proportion.

To solve a problem using proportional reasoning, it’s important to identify that one quantity or size is related to another one by a determined ratio in that situation.


During a recent trip, Robert drove 483 kilometres in 7 hours.

  • What was his average speed during the trip?
  • If he drove at the same average speed, what distance would he cover in 10 hours?

Example of solution:

The average speed is the number of kilometres covered by a unit of time, which in this case is one hour.
Here, Robert drove a distance of 483 km in 7 hours.
His speed, in kilometres per hour (km/h), can be obtained by examining the ratio:


  • Because 483÷ 7 = 69, his average speed was 69 km/h.
  • The distance covered in 10 hours can be found by considering the proportion: \(\dfrac {483} {7}=\dfrac {x} {10}\).
    Therefore, we find: \(x = 69 × 10 = 690\). Robert would drive 690 km in 10 hours.

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