These worksheets are free forever. Want lessons that adapt to your child as they learn, plus progress tracking? Try Ignition Learning free.

Ignition Learning — Activity Sheet

Rates & proportion

Mathematics · Year 9

Name: ______________________Date: ____________

A rate compares two different quantities with different units, like km/h or $/kg. A unit rate expresses this per single unit (e.g. "cost per item"), making comparisons easy. Direct proportion means two quantities increase or decrease together at a constant rate — if you double one, the other doubles too, like the relationship between distance, speed and time (distance = speed × time).

Example

A car travels 240km in 3 hours — that's a rate of 240 ÷ 3 = 80km/h. At that same speed, travelling for 5 hours would cover 80 × 5 = 400km — the distance and time are directly proportional at a constant speed.

Key terms

Rate:: A comparison of two different quantities with different units.
Unit rate:: A rate expressed per single unit, e.g. cost per item.
Direct proportion:: When two quantities increase or decrease together at a constant rate.

Questions

1. A rate compares:
- Two different quantities with different units
- Two identical quantities
- Only whole numbers
- A single quantity
2. Km/h is an example of a:
- Rate
- Fraction only
- Ratio with identical units
- Percentage
3. A car travels 100km in 2 hours. What is its speed?
- 50km/h
- 100km/h
- 200km/h
- 2km/h
4. Distance = Speed ×:
- Time
- Weight
- Colour
- Money
5. A unit rate expresses a rate:
- Per single unit
- Per 100 units only
- As a percentage always
- As a whole number only
6. 6 apples cost $3. What is the unit rate (cost per apple)?
- $0.50
- $2
- $3
- $6
7. Direct proportion means two quantities:
- Increase or decrease together at a constant rate
- Are always exactly equal
- Have no relationship
- Always decrease together
8. A car travels 240km in 3 hours. What is its speed?
- 60km/h
- 80km/h
- 100km/h
- 120km/h
9. At 80km/h, how far would a car travel in 5 hours?
- 160km
- 320km
- 400km
- 480km
10. 4kg of apples costs $12. What is the cost per kg?
- $2
- $3
- $4
- $48
11. If 3 items cost $18, how much would 5 items cost at the same rate?
- $24
- $30
- $36
- $90
12. A tap fills a 60L tub in 12 minutes. What is the fill rate per minute?
- 3L
- 5L
- 6L
- 12L
13. If two quantities are directly proportional and one doubles, the other:
- Also doubles
- Halves
- Stays the same
- Becomes zero
14. A recipe for 4 people uses 200g of rice. How much rice for 10 people, at the same rate?
- 400g
- 500g
- 600g
- 800g
15. A car uses 40L of fuel to travel 480km. At the same rate, how far could it travel on 25L?
- 200km
- 250km
- 300km
- 350km
16. Worker A paints a fence in 6 hours; Worker B paints an identical fence in 4 hours. Working together at their individual rates, are they faster or slower than either alone?
- Faster than either alone
- Slower than either alone
- Exactly the same as Worker A alone
- Impossible to determine
17. A photocopier prints 45 pages in 3 minutes. How many pages could it print in 8 minutes at the same rate?
- 100
- 110
- 120
- 135
18. Two cars leave the same point, one at 60km/h and one at 80km/h, travelling in the same direction. After 3 hours, how far apart are they?
- 20km
- 40km
- 60km
- 80km
19. A 500g bag of flour costs $2.50, and a 750g bag costs $3.30. Which is the better value per gram?
- The 750g bag
- The 500g bag
- They are identical value
- Cannot be determined
20. A hose fills a pool at 25L per minute. How long will it take to fill a 3,000L pool?
- 100 minutes
- 120 minutes
- 150 minutes
- 200 minutes
21. If y is directly proportional to x, and y = 12 when x = 4, what is y when x = 10?
- 24
- 28
- 30
- 32

Answer key (parent copy)

1. Two different quantities with different units
2. Rate
3. 50km/h
4. Time
5. Per single unit
6. $0.50
7. Increase or decrease together at a constant rate
8. 80km/h
9. 400km
10. $3
11. $30
12. 5L
13. Also doubles
14. 500g
15. 300km
16. Faster than either alone
17. 120
18. 60km
19. The 750g bag
20. 150 minutes
21. 30