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Secondary 1 Mathematics · Ratios and rates

Name: ______________________

Date: ____________

1. Simplify the ratio 15 : 25.
- ☐ (a) 3 : 5
- ☐ (b) 5 : 3
- ☐ (c) 1 : 2
- ☐ (d) 3 : 4
2. A class has 12 girls and 8 boys. What is the ratio of boys to girls in simplest form?
- ☐ (a) 3 : 2
- ☐ (b) 2 : 3
- ☐ (c) 8 : 20
- ☐ (d) 12 : 8
3. Which ratio is equivalent to 4 : 6?
- ☐ (a) 8 : 10
- ☐ (b) 2 : 3
- ☐ (c) 6 : 4
- ☐ (d) 1 : 2
4. A car travels 240 km in 3 hours. What is its average speed?
- ☐ (a) 60 km/h
- ☐ (b) 80 km/h
- ☐ (c) 720 km/h
- ☐ (d) 243 km/h
5. $60 is shared in the ratio 1 : 3. How much is the larger share?
6. Simplify the ratio 18 : 24.
7. 4 kg of apples cost $14. What is the cost per kilogram?
8. A recipe uses flour and sugar in the ratio 5 : 2. How many grams of sugar are needed for 300 g of flour?

Answer sheet

1. 3 : 5 — The highest common factor is 5. 15 ÷ 5 = 3 and 25 ÷ 5 = 5, so 15 : 25 = 3 : 5.
2. 2 : 3 — Boys come first: 8 : 12. Dividing both by 4 gives 2 : 3.
3. 2 : 3 — Dividing both parts of 4 : 6 by 2 gives 2 : 3.
4. 80 km/h — Speed is distance ÷ time: 240 ÷ 3 = 80 km/h.
5. $45 — There are 1 + 3 = 4 parts. One part is $60 ÷ 4 = $15, so the larger share is 3 × $15 = $45.
6. 3 : 4 — The highest common factor of 18 and 24 is 6. 18 ÷ 6 = 3 and 24 ÷ 6 = 4.
7. $3.50 per kg — $14 ÷ 4 = $3.50 per kilogram.
8. 120 g — 5 parts = 300 g, so 1 part = 60 g. Sugar is 2 parts: 2 × 60 = 120 g.