Ratio and Proportion Worksheet - Free Printable

Let's solve each problem step by step on the Ratio and Proportion Sheet 3. For each question, we'll:

1. Count the number of each object.
2. Write the ratio of one to the other (simplified if possible).
3. Find the proportion of each object as a fraction of the total set.

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1) Butterflies and Flies

- Butterflies: 5
- Flies: 3
- Total: 5 + 3 = 8

Ratio of butterflies to flies = 5 : 3
Proportion of butterflies = 5/8
Proportion of flies = 3/8

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2) Rabbits and Cats

- Rabbits: 5
- Cats: 6
- Total: 5 + 6 = 11

Ratio of rabbits to cats = 5 : 6
Proportion of rabbits = 5/11
Proportion of cats = 6/11

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3) Snails and Frogs

- Snails: 4
- Frogs: 6
- Total: 4 + 6 = 10

Ratio of snails to frogs = 4 : 6 → Simplify by dividing both by 2 → 2 : 3
Proportion of snails = 4/10 = 2/5
Proportion of frogs = 6/10 = 3/5

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4) Rockets and Stars

- Rockets: 4
- Stars: 6
- Total: 4 + 6 = 10

Ratio of rockets to stars = 4 : 6 → Simplify → 2 : 3
Proportion of rockets = 4/10 = 2/5
Proportion of stars = 6/10 = 3/5

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5) Bicycles and Cars

- Bicycles: 7
- Cars: 7
- Total: 7 + 7 = 14

Ratio of bicycles to cars = 7 : 7 → Simplify → 1 : 1
Proportion of bicycles = 7/14 = 1/2
Proportion of cars = 7/14 = 1/2

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6) Triangles and Hexagons

- Triangles: 6
- Hexagons: 5
- Total: 6 + 5 = 11

Ratio of triangles to hexagons = 6 : 5
Proportion of triangles = 6/11
Proportion of hexagons = 5/11

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✔ Final Answers:

| Question | Ratio | Proportion of First | Proportion of Second |
|--------|-------|----------------------|-----------------------|
| 1) | 5 : 3 | 5/8 | 3/8 |
| 2) | 5 : 6 | 5/11 | 6/11 |
| 3) | 2 : 3 | 2/5 | 3/5 |
| 4) | 2 : 3 | 2/5 | 3/5 |
| 5) | 1 : 1 | 1/2 | 1/2 |
| 6) | 6 : 5 | 6/11 | 5/11 |

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🔍 Explanation Summary:

- Ratio compares two quantities (e.g., A:B).
- Proportion is how much of the whole each part represents, written as a fraction.
- Always simplify ratios and fractions when possible.
- The sum of proportions should always equal 1 (or 100%).

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