# 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.

### Example

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:

$$\dfrac{\textrm{distance}}{\textrm{duration}}=\dfrac{483}{7}$$.

• 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.