Percentages and ratio · Ages 13–14

Rates worksheet

Part of: Rates, ratios & proportions

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Percentages and ratio · Ages 13–14

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Name:Date:Score:／48

Write each answer in the space. For word problems, show your working and write a sentence answer.

1.3 ballpoint pens cost $60: $ each, and 7 of them cost $.
Fill in each blank
Answer:
2.9 kg of rice costs $279: unit price = $kg
Answer:
3.2 ballpoint pens cost $46: $ each, and 5 of them cost $.
Fill in each blank
Answer:
4.18 km/h = m/s
Answer:
5.108 km/h = m/s
Answer:
6.A car uses 8 L of petrol every 100 km, and petrol costs $22 a litre. What does petrol for 600 km cost?
Answer:
7.A car uses 12 L of petrol every 100 km, and petrol costs $21 a litre. What does petrol for 300 km cost?
Answer:

8.A car travels 220 km in 4 hours: its average speed is 55 km/h.
True or false?
Answer:
9.A printer prints 243 pages in 9 minutes. What is its printing rate?
- A. 252 pages a minute
- B. 27 pages a minute
- C. 234 pages a minute
- D. 2187 pages a minute
Choose the right answer
Answer:
10.A car travels 120 km in 2 hours: its average speed is 60 km/h.
True or false?
Answer:
11.The same cereal: a small box of 500 g costs $70, a big box of 750 g costs $75. Which is the better buy?
- A. They are as good as each other
- B. The big box
- C. The small box
- D. They can't be compared
Choose the right answer
Answer:
12.How many m/s is 54 km/h?
- A. 15 m/s
- B. 900 m/s
- C. 194.4 m/s
- D. 54000 m/s
Choose the right answer
Answer:

13.Printer A prints 29 pages a minute and printer B 21. Working together, how many minutes do they take over a 350-page document?
Working:
Answer:
14.One laundry liquid comes in three sizes: 500 mL for $46, 1.25 L for $100, 2 L for $136. Which is the best buy?
- A. The 500 mL bottle
- B. They are all as good
- C. The 1.25 L bottle
- D. The 2 L bottle
Choose the right answer
Working:
Answer:
15.A worker lays 6 m² of floor tiles an hour. With 6 workers together, how many hours does 324 m² take?
Working:
Answer:
16.A tap lets in 30 L of water a minute. How many minutes does it take to fill an empty tank that holds 480 L?
Working:
Answer:
17.Turn 108 km/h into m/s. Put the steps in order.
- A. 108 km = 108000 m
- B. 108000 ÷ 3600 = 30
- C. 1 hour = 3600 seconds
Write the letters in the right order
Working:
Answer:
18.Ka-lok's dad drives 275 km in 5 hours. His average speed is km/h; at that speed, he covers km in 3 hours.
Fill in each blank
Working:
Answer:

Show the answers and working

Rates worksheet: Answers and working

1. 20, 140
The unit rate first: 60 ÷ 3 = 20; then 20 × 7 = 140.
2. 31
Unit price = price ÷ weight = 279 ÷ 9 = 31, that is $31 a kg.
3. 23, 115
The unit rate first: 46 ÷ 2 = 23; then 23 × 5 = 115.
4. 5
1 km = 1000 m and 1 hour = 3600 seconds: 18 × 1000 ÷ 3600 = 5. Both units change.
5. 30
1 km = 1000 m and 1 hour = 3600 seconds: 108 × 1000 ÷ 3600 = 30. Both units change.
6. 1056 dollars
Petrol used: 600 ÷ 100 × 8 = 48 L, costing 48 × 22 = 1056 dollars. Two rates, one after the other.
7. 756 dollars
Petrol used: 300 ÷ 100 × 12 = 36 L, costing 36 × 21 = 756 dollars. Two rates, one after the other.

8. True
Speed = distance ÷ time = 220 ÷ 4 = 55 km/h. Distance and time are different quantities: divide them.
9. B. 27 pages a minute
Printing rate = pages ÷ time = 243 ÷ 9 = 27 pages a minute.
10. True
Speed = distance ÷ time = 120 ÷ 2 = 60 km/h. Distance and time are different quantities: divide them.
11. B. The big box
Per 100 g: the small box 70 ÷ 500 × 100 = $14, the big box 75 ÷ 750 × 100 = $10. The one cheaper per unit is the better buy.
12. A. 15 m/s
54 × 1000 ÷ 3600 = 15: 1000 ÷ 3600 is 1 ÷ 3.6.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 7 minutes
Together they print 29 + 21 = 50 pages a minute, and 350 ÷ 50 = 7 minutes. Rates add here: they work through the same minutes.
14. D. The 2 L bottle
In mL, the price per 250 mL: 46 ÷ 2 = 23, 100 ÷ 5 = 20, 136 ÷ 8 = 17. The cheapest is $17 per 250 mL.
15. 9 hours
6 workers lay 6 × 6 = 36 m² an hour together, and 324 ÷ 36 = 9 hours.
16. 16 minutes
Time = volume ÷ rate = 480 ÷ 30 = 16 minutes.
17. A → C → B
km into m, then hours into seconds, then divide: 108 km/h = 30 m/s.
18. 55, 165
Speed = 275 ÷ 5 = 55 km/h; distance = 55 × 3 = 165 km.

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