Ratio and Proportional Reasoning

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📊 Part 1: Understanding Ratios

1. In a box of marbles, there are 3 red marbles for every 5 blue marbles. If there are 15 red marbles, how many blue marbles are there?

20 blue marbles

25 blue marbles

30 blue marbles

18 blue marbles

2. A recipe calls for 2 cups of flour for every 3 cups of sugar. Which of these are equivalent ratios? (Select all that apply)

4 cups flour : 6 cups sugar

6 cups flour : 9 cups sugar

3 cups flour : 2 cups sugar

10 cups flour : 15 cups sugar

3. In a cricket team, the ratio of bowlers to batsmen is 2:3. If there are 8 bowlers, how many total players are there?

12 players

20 players

16 players

24 players

4. Sarah and Jake are sharing 120 stickers. For every 1 sticker Sarah gets, Jake gets 4 stickers. How many stickers does Sarah get?

🎨 Part 2: Ratio Problems and Bar Models

5. Draw a bar model to represent the ratio 3:7 and use it to solve: If the smaller quantity is 12, what is the larger quantity?

Answer: The larger quantity is _____________

6. A paint mixture uses red and white paint in the ratio 2:5. If you need 21 litres of paint mixture in total, how much of each colour do you need?

Red paint: _____________ litres

White paint: _____________ litres

7. In a school fundraiser, the money raised is shared between the library and sports equipment in the ratio 3:4. If the library receives $450, how much money was raised in total?

Total money raised: $______________

8. Explain in your own words what a ratio tells us about the relationship between two quantities.

🌟 Part 3: Real-Life Applications

9. A New Zealand rugby team has forwards and backs in the ratio 8:7. If there are 45 players in the squad, how many forwards and how many backs are there?

Forwards: _____________ players

Backs: _____________ players

10. At a school hangi, the ratio of kumara to potatoes is 2:3. If 60 kg of vegetables are needed in total, how much kumara and how many potatoes should be prepared?

Kumara: _____________ kg

Potatoes: _____________ kg