Australian Curriculum v9 / ACiQ Year 7 Mathematics - Unit 1 - Ratios, rates and percentages
Ratios, Rates and Percentages | Year 7 Mathematics
Use ratios, unit rates and percentages to compare quantities and solve practical Year 7 problems.
Updated 2026-06-15 - 4 min read
Ratios, rates and percentages are all ways to compare quantities. The important habit is to ask what is being compared before doing any calculation.
Ratios compare parts
A ratio such as $3:2$ means there are 3 parts of one quantity for every 2 parts of another quantity. The parts do not have to be the actual amounts. They show the relationship.
If a cordial recipe uses 3 cups of water for every 2 cups of cordial, the total mixture has 5 parts. Water is 3 of those 5 parts.
That means:
- water is $\frac{3}{5}$ of the mixture
- cordial is $\frac{2}{5}$ of the mixture
- the water-to-cordial ratio is $3:2$
Rates compare different units
A rate compares quantities measured in different units.
Examples:
- 60 kilometres per hour
- \$4 per kilogram
- 12 pages per minute
- 3 goals per game
A unit rate tells you the amount for one unit. Unit rates make comparisons fair.
Percentages need a base
A percentage is always a percentage of something. That "something" is the base.
If a \$40 shirt is discounted by 25 percent, the base is \$40.
25 percent of $40 is:
$0.25 \times 40 = 10$
The discount is \$10, so the sale price is \$30.
If the shirt then increases by 25 percent from \$30, the base is now \$30, not \$40.
$0.25 \times 30 = 7.50$
The new price is \$37.50, not \$40.
This is why repeated percentage change needs careful thinking.
Choosing the clearest comparison
Many problems can be described in more than one way, but one comparison is usually clearest.
Use a ratio when the relationship between parts matters. A paint mixture of blue and white in the ratio $2:5$ is about how the two parts compare.
Use a rate when two different units are connected. Speed uses kilometres and hours. Unit price uses dollars and kilograms. Reading speed might use pages and minutes.
Use a percentage when a part is compared with a whole or a change is compared with a starting amount. A test score of 18 out of 24 can become 75 percent because the score is being compared with the whole test.
This choice matters in worded problems. If a question asks which shop is better value, a unit rate is usually best. If it asks what part of a mixture is cordial, a fraction or percentage of the whole may be better than the original ratio.
Quick check
- A smoothie uses yoghurt and fruit in the ratio $2:3$. What fraction of the smoothie is fruit?
- A 750 g packet costs \$6. What is the price per 100 g?
- A \$90 pair of shoes is discounted by 20 percent. What is the sale price?
Answers:
- Fruit is $\frac{3}{5}$ of the smoothie.
- $6 \div 7.5 = 0.80$, so the price is \$0.80 per 100 g.
- 20 percent of \$90 is \$18, so the sale price is \$72.
Transfer task
Choose a real comparison from shopping, sport, travel or cooking. Decide whether a ratio, rate or percentage is the clearest model, then explain why that model makes the comparison fair.