Ratios and proportions

01Why this matters

Mixing drinks, scaling recipes and comparing maps all depend on preserving relative amounts.

02See it

03Understand it

A ratio compares quantities multiplicatively. A proportion states that two ratios are equal.

The ratio 2:3 means two parts of one quantity for every three parts of another. There are five parts altogether. Ratios can be scaled by multiplying every term by the same positive number. Keep track of whether the ratio is part-to-part or part-to-whole: these are not interchangeable.

04Guided example

A drink uses concentrate and water in the ratio 1:4. How much of each makes 1 litre?

1. Count the total parts: 1 + 4 = 5. Convert the total to 1,000 mL.
2. One part is 1,000 ÷ 5 = 200 mL.
3. Use 200 mL concentrate and 4 × 200 = 800 mL water. Their total is 1,000 mL.

05Try it

06Practise it

07Use it in the real world

A recipe for 4 people needs 300 g of rice. For 6 people the scale factor is 6/4 = 1.5, so use 450 g, assuming the same serving size.

08Quick check

09Summary

A ratio compares quantities multiplicatively. A proportion states that two ratios are equal. Use 200 mL concentrate and 4 × 200 = 800 mL water. Their total is 1,000 mL.

Before moving on, explain the worked example in your own words. Use the hint on any question you want to revisit.

10Key idea