2. Proportional Reasoning Problems on Ratios and Rates Rates Ratio 10 20 30 40 50 10 20 30 40 50 10 20 30 40 50 10 20 30 40 50

3. Ratios – Level 1 Give the ratio of circles to rectangles. Answer: 3: 5

4. Ratios – Level 2 Give the ratio of blue circles to red triangles to rectangles Answer: 3 : 1 : 0

5. Ratios – Level 3 Give the simplest form of the ratio 15 : 25 and another equivalent ratio. Answer: simplest form = 3:5 another equivalent ratio = 30:50

6. Ratios – Level 4 What is the percentage of blue circles present In the following diagram. Answer: 3 : 10 = 3÷10 = 0.3 = 30%

7. Ratios – Level 5 There are 3 colored marbles in a bag. The color of the marbles are blue, red and green. If the part to part ratio of blue marbles to red marbles is 3 : 5 and the part to whole ratio of blue marbles to the total marbles is 3:15. How many green marbles are there in the bag? Answer: 7

8. Rates – Level 1 Which of the following is an example of a rate A) $15 per 1 medium pizza B) 30 km to 10 inches C) 10 green marbles to 3 red marbles Answer: $15 per 1 medium pizza

9. Rates – Level 2 Define the term unit rate. Answer: Unit rate describes how many units of a type of quantity to one unit of a different type of quantity.

10. Rates – Level 3 What is the unit rate of 90 meters in 15 seconds? Answer: 6 meters per 1 second

11. Rates – Level 4 John can eat 50 timbits in 1 minute. How much can John eat in 15 seconds? Answer: 12.5 timbits

12. Rates – Level 5 What is the mistake in this solution? Answer: Step 2 Silva is able to jog 1500 meters in 5 min. What is the unit rate of Silva’s speed. Step 1: 5 min ÷ 5 = 1 min Step 2: 1500 m × 5 = 7500 m Solution = 7500m in 1 min

13. Problems on Ratios and Rates – Level 1 15 : 5 = 45 : S Answer: S =15

14. Problems on Ratios and Rates – Level 2 If John earns $24 in one hour, how much will he earn if he works 25 hours? Answer: $ 600

15. Problems on Ratios and Rates – Level 3 13 : 8 = x : 34 Answer: x = 55.25

16. Problems on Ratios and Rates – Level 4 If a baker bakes 200 croissants in 2 hours, how many croissants can a baker make given 7 hours? Answer: 700 croissants

17. Problems on Ratios and Rates – Level 5 Is the following ratio equivalent? Is there a solution for x? 2 : 5 : 8 | 26 : x : 104 Answer: x = 65 Yes, because 2 × 13 = 26 and 8 × 13 = 104

18. Proportional Reasoning – Level 1 In a shootout, Luongo allowed 2 out of 3 shootout goals while Hiller allowed 1 out of 3 shootout goals. Who had a better save percentage? Answer: Hiller – 2/3

19. Proportional Reasoning – Level 2 If paint A has 3 cans of red paint and 4 cans of white paint and paint B uses 6 cans of red paint and 8 cans of white paint. Which solution will have a stronger red color? Answer: Same

20. Proportional Reasoning – Level 3 Which yields the greatest speed? Answer: 200 meters in 21 seconds a) 50 meters in 7 seconds b) 100 meters 12 seconds c) 200 meters in 21 seconds

21. Proportional Reasoning – Level 4 Jenny wanted to buy a sack of potatoes. Superstore has a 5 kg sack for $3.99 while Safeway has a 2 kg for $1.99. Where should Jenny buy the sack of potatoes? Answer: Superstore

22. Proportional Reasoning – Level 5 Ryan needs a winter jacket for next winter. Store A is selling a wool coat for $320. There is an additional sale of 30% off on everything in Store A. Store B sells a different coat for $240. The store is also offering an additional 10% off. Which jacket should Ryan buy if he Is looking for the cheaper jacket? Answer: Store B

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