Covers the Year 7 ratio and rates skills students use in cooking, maps, speed and shopping: simplifying ratios (including ones with different units), finding equivalent ratios, dividing a quantity in a given ratio, calculating unit rates and speed, and comparing best buys. Every example is checked.
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Curriculum: Australian Curriculum. We show specific outcome codes only where they have been verified against the official curriculum document.
Completed: Ratio and Rates
Year 7 students (typically ages 12–13) working on ratio & rates. It is pitched at level 2 · standard.
This is a study guide, so there is no separate answer sheet; the 'Check yourself' questions include answers.
About 20 minutes. Short, regular sessions work best: two or three a week beats one long one.
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Try Year 7 Ratio Worksheet — Level 1.
Year 7 · Mathematics · Ratio & Rates
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A ratio compares amounts of the same kind. Cordial mixed 1 : 4 means 1 part cordial for every 4 parts water. Order matters: 1 : 4 is not the same as 4 : 1. Ratios are simplified like fractions, by dividing every part by the same number, and the parts must be in the same units before you simplify. A rate compares two different kinds of quantity, such as kilometres per hour or dollars per kilogram.
Simplify 12 : 18 and 250 g : 1 kg
Equivalent ratios. Multiplying or dividing both parts by the same number gives an equivalent ratio: 2 : 3 = 4 : 6 = 10 : 15. This is how you scale a recipe. If 2 cups of flour go with 3 cups of milk, then 8 cups of flour (2 × 4) need 3 × 4 = 12 cups of milk. Check: 8 : 12 simplifies back to 2 : 3.
Dividing a quantity in a ratio. Add the parts of the ratio to find the total number of parts, divide the quantity by that total to find the value of one part, then multiply to find each share. Always check that the shares add back to the original amount.
Share $120 between Ava and Ben in the ratio 3 : 5
A car travels 180 km in 2.5 hours. What is its average speed, and how far would it go in 4 hours at that speed?
Best buy: 500 g of rice for $2.40 or 2 kg of rice for $9.00?
| Ratio | First part as a fraction of the total | Second part as a fraction of the total |
|---|---|---|
| 1 : 1 | ||
| 1 : 3 | ||
| 2 : 3 | ||
| 3 : 7 |
Answers: 1. 3 : 5 2. 1 : 5 (40 : 200) 3. 15 4. 16 and 40 (7 parts, so one part is 8) 5. 62.5 km/h 6. 10 apples for $6.50 (65 cents each, compared with 70 cents each)
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Simplify ratios, divide amounts in a given ratio and solve ratio problems. Builds confidence with the core skill before adding complexity.…
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