Math worksheet for practicing ratios and proportions with visual objects.

Let's solve each problem step by step from the Ratio and Proportion Sheet 6. We'll count the objects, express ratios in lowest terms, and find proportions as simplified fractions.

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Problem 1)

Objects:
○ ○ □ △ □ △ ○ □ ○ ○

Count:
- Circles (○): 5
- Triangles (△): 2
- Squares (□): 3

Total = 5 + 2 + 3 = 10

Ratio of ○ to △ to □
= 5 : 2 : 3 → Already in lowest terms.

Proportions:
- Proportion of ○ = $ \frac{5}{10} = \frac{1}{2} $
- Proportion of △ = $ \frac{2}{10} = \frac{1}{5} $
- Proportion of □ = $ \frac{3}{10} $

✔ Answer:
- Ratio: 5 : 2 : 3
- Proportion of ○ = 1/2
- Proportion of △ = 1/5
- Proportion of □ = 3/10

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Problem 2)

Objects:
Ants (🐜), Butterflies (🦋), Snails (🐌)

Sequence: 🐜 🐜 🦋 🐜 🐌 🦋 🐜 🦋 🐜 🦋 🐌 🐜

Count:
- Ants (🐜): 6
- Butterflies (🦋): 4
- Snails (🐌): 2

Total = 6 + 4 + 2 = 12

Ratio of 🦋 to 🐌 to 🐜
= 4 : 2 : 6 → Simplify by dividing by 2 → 2 : 1 : 3

Proportions:
- Proportion of 🦋 = $ \frac{4}{12} = \frac{1}{3} $
- Proportion of 🐌 = $ \frac{2}{12} = \frac{1}{6} $
- Proportion of 🐜 = $ \frac{6}{12} = \frac{1}{2} $

✔ Answer:
- Ratio: 2 : 1 : 3
- Proportion of 🦋 = 1/3
- Proportion of 🐌 = 1/6
- Proportion of 🐜 = 1/2

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Problem 3)

Objects: Footballs (🏈), Basketballs (🏀), Soccer balls (⚽)

Sequence: 🏈 🏀 🏀 ⚽ 🏈 🏀 🏈 🏀 🏈 🏀 ⚽ 🏈 🏈

Count:
- Footballs (🏈): 5
- Basketballs (🏀): 5
- Soccer balls (⚽): 2

Total = 5 + 5 + 2 = 12

Ratio of 🏈 to 🏀 to ⚽
= 5 : 5 : 2 → Already in lowest terms.

Proportions:
- Proportion of 🏈 = $ \frac{5}{12} $
- Proportion of 🏀 = $ \frac{5}{12} $
- Proportion of ⚽ = $ \frac{2}{12} = \frac{1}{6} $

✔ Answer:
- Ratio: 5 : 5 : 2
- Proportion of 🏈 = 5/12
- Proportion of 🏀 = 5/12
- Proportion of ⚽ = 1/6

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Problem 4)

Objects: Bicycles (🚲), Cars (🚗), Tractors (🚜)

Sequence:
Row 1: 🚗 🚗 🚜 🚲 🚗 🚲 🚗 🚲 🚗 🚲 🚗 🚲 🚜
Row 2: 🚗 🚲 🚲 🚲 🚗 🚲 🚲 🚲 🚗 🚲 🚲 🚲 🚜

Wait — let’s count carefully:

From both rows:

- Cars (🚗): Let's count:
- Row 1: 4 cars (positions 1,2,5,8,10,11? Wait — recheck)
Actually, better to list all:

List all items:

1. 🚗
2. 🚗
3. 🚜
4. 🚲
5. 🚗
6. 🚲
7. 🚗
8. 🚲
9. 🚗
10. 🚲
11. 🚗
12. 🚲
13. 🚜
14. 🚗
15. 🚲
16. 🚲
17. 🚲
18. 🚗
19. 🚲
20. 🚲
21. 🚲
22. 🚗
23. 🚲
24. 🚲
25. 🚲
26. 🚜

Now count:

- Cars (🚗): positions 1,2,5,7,9,11,14,18,22 → 9 cars
- Bicycles (🚲): positions 4,6,8,10,12,15,16,17,19,20,21,23,24,25 → 14 bikes
- Tractors (🚜): positions 3,13,26 → 3 tractors

Total = 9 + 14 + 3 = 26

Ratio of 🚲 to 🚗 to 🚜
= 14 : 9 : 3 → Check if reducible: GCF of 14,9,3 is 1 → already in lowest terms.

Proportions:
- Proportion of 🚲 = $ \frac{14}{26} = \frac{7}{13} $
- Proportion of 🚗 = $ \frac{9}{26} $
- Proportion of 🚜 = $ \frac{3}{26} $

✔ Answer:
- Ratio: 14 : 9 : 3
- Proportion of 🚲 = 7/13
- Proportion of 🚗 = 9/26
- Proportion of 🚜 = 3/26

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Problem 5)

Objects: Circles with different patterns:
- Striped (🟥) — blue stripes
- White (⚪)
- Solid dark blue (🟦)

Sequence:
🟥 🔵 ⚪ 🟥 🔵 ⚪ 🟥 🟦 ⚪ 🟥 🔵 ⚪ 🟥 🟦 ⚪ ⚪ ⚪

Wait — let's list them clearly:

1. 🟥 (striped)
2. 🔵 (solid blue)
3. ⚪ (white)
4. 🟥
5. 🔵
6. ⚪
7. 🟥
8. 🟦 (dark blue)
9. ⚪
10. 🟥
11. 🔵
12. ⚪
13. 🟥
14. 🟦
15. ⚪
16. ⚪
17. ⚪

Now count:

- Striped (🟥): positions 1,4,7,10,13 → 5
- Solid Blue (🔵): positions 2,5,11 → 3
- White (⚪): positions 3,6,9,12,15,16,17 → 7

Total = 5 + 3 + 7 = 15

Ratio of 🟥 to ⚪ to 🔵
= 5 : 7 : 3 → Already in lowest terms.

Proportions:
- Proportion of 🟥 = $ \frac{5}{15} = \frac{1}{3} $
- Proportion of ⚪ = $ \frac{7}{15} $
- Proportion of 🔵 = $ \frac{3}{15} = \frac{1}{5} $

✔ Answer:
- Ratio: 5 : 7 : 3
- Proportion of 🟥 = 1/3
- Proportion of ⚪ = 7/15
- Proportion of 🔵 = 1/5

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✔ Final Answers Summary:

#### 1)
- Ratio: 5 : 2 : 3
- Proportion of ○ = 1/2
- Proportion of △ = 1/5
- Proportion of □ = 3/10

#### 2)
- Ratio: 2 : 1 : 3
- Proportion of 🦋 = 1/3
- Proportion of 🐌 = 1/6
- Proportion of 🐜 = 1/2

#### 3)
- Ratio: 5 : 5 : 2
- Proportion of 🏈 = 5/12
- Proportion of 🏀 = 5/12
- Proportion of ⚽ = 1/6

#### 4)
- Ratio: 14 : 9 : 3
- Proportion of 🚲 = 7/13
- Proportion of 🚗 = 9/26
- Proportion of 🚜 = 3/26

#### 5)
- Ratio: 5 : 7 : 3
- Proportion of 🟥 = 1/3
- Proportion of ⚪ = 7/15
- Proportion of 🔵 = 1/5

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