Ratios Worksheet for students to practice making equivalent ratios by filling in missing values.
A math worksheet titled "Ratios Worksheet" with ten problems requiring students to fill in blanks to make ratios equivalent, featuring a clean layout with numbered questions and blank spaces for answers.
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ID: #572238
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Step-by-step solution for: Ratio Worksheets - Math Monks
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Show Answer Key & Explanations
Step-by-step solution for: Ratio Worksheets - Math Monks
Let's solve each problem step by step. The goal is to fill in the blanks so that each ratio is equivalent to the original one.
We'll use the concept of equivalent ratios, which means multiplying or dividing both terms of the ratio by the same number.
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Start with 1:2
- To get from 2 to 4 → multiply by 2 → $1 \times 2 = 2$ → 2:4
- To get from 2 to 6 → multiply by 3 → $1 \times 3 = 3$ → 3:6
- From 1 to 4 → multiply by 4 → $2 \times 4 = 8$ → 4:8
- From 2 to 10 → multiply by 5 → $1 \times 5 = 5$ → 5:10
- From 1 to 6 → multiply by 6 → $2 \times 6 = 12$ → 6:12
✔ Answer:
1 : 2 = 2 : 4 = 3 : 6 = 4 : 8 = 5 : 10 = 6 : 12
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Original: 1:3
- 3 → 6 → ×2 → $1 \times 2 = 2$ → 2:6
- 1 → 3 → ×3 → $3 \times 3 = 9$ → 3:9
- 3 → 12 → ×4 → $1 \times 4 = 4$ → 4:12
- 1 → 5 → ×5 → $3 \times 5 = 15$ → 5:15
- 1 → 6 → ×6 → $3 \times 6 = 18$ → 6:18
✔ Answer:
1 : 3 = 2 : 6 = 3 : 9 = 4 : 12 = 5 : 15 = 6 : 18
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Original: 1:7
- 7 → 14 → ×2 → $1 \times 2 = 2$ → 2:14
- 7 → 21 → ×3 → $1 \times 3 = 3$ → 3:21
- 1 → 4 → ×4 → $7 \times 4 = 28$ → 4:28
- 1 → 5 → ×5 → $7 \times 5 = 35$ → 5:35
- 7 → 42 → ×6 → $1 \times 6 = 6$ → 6:42
✔ Answer:
1 : 7 = 2 : 14 = 3 : 21 = 4 : 28 = 5 : 35 = 6 : 42
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Original: 2:5
- 5 → 10 → ×2 → $2 \times 2 = 4$ → 4:10
- 5 → 15 → ×3 → $2 \times 3 = 6$ → 6:15
- 2 → 8 → ×4 → $5 \times 4 = 20$ → 8:20
- 5 → 25 → ×5 → $2 \times 5 = 10$ → 10:25
- 5 → 30 → ×6 → $2 \times 6 = 12$ → 12:30
✔ Answer:
2 : 5 = 4 : 10 = 6 : 15 = 8 : 20 = 10 : 25 = 12 : 30
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Simplify 2:4 → 1:2
But we can work directly:
- 4 → 8 → ×2 → $2 \times 2 = 4$ → 4:8
- 4 → 12 → ×3 → $2 \times 3 = 6$ → 6:12
- 2 → 8 → ×4 → $4 \times 4 = 16$ → 8:16
- 4 → 20 → ×5 → $2 \times 5 = 10$ → 10:20
- 2 → 12 → ×6 → $4 \times 6 = 24$ → 12:24
✔ Answer:
2 : 4 = 4 : 8 = 6 : 12 = 8 : 16 = 10 : 20 = 12 : 24
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Original: 5:9
- 5 → 10 → ×2 → $9 \times 2 = 18$ → 10:18
- 5 → 15 → ×3 → $9 \times 3 = 27$ → 15:27
- 5 → 20 → ×4 → $9 \times 4 = 36$ → 20:36
- 5 → 25 → ×5 → $9 \times 5 = 45$ → 25:45
- 9 → 54 → ×6 → $5 \times 6 = 30$ → 30:54
✔ Answer:
5 : 9 = 10 : 18 = 15 : 27 = 20 : 36 = 25 : 45 = 30 : 54
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Original: 1:5
- 5 → 10 → ×2 → $1 \times 2 = 2$ → 2:10
- 1 → 3 → ×3 → $5 \times 3 = 15$ → 3:15
- 1 → 4 → ×4 → $5 \times 4 = 20$ → 4:20
- 1 → 5 → ×5 → $5 \times 5 = 25$ → 5:25
- 1 → 6 → ×6 → $5 \times 6 = 30$ → 6:30
✔ Answer:
1 : 5 = 2 : 10 = 3 : 15 = 4 : 20 = 5 : 25 = 6 : 30
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Original: 3:2
- 2 → 4 → ×2 → $3 \times 2 = 6$ → 6:4
- 2 → 6 → ×3 → $3 \times 3 = 9$ → 9:6
- 3 → 12 → ×4 → $2 \times 4 = 8$ → 12:8
- 2 → 10 → ×5 → $3 \times 5 = 15$ → 15:10
- 3 → 18 → ×6 → $2 \times 6 = 12$ → 18:12
✔ Answer:
3 : 2 = 6 : 4 = 9 : 6 = 12 : 8 = 15 : 10 = 18 : 12
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Original: 1:8
- 8 → 16 → ×2 → $1 \times 2 = 2$ → 2:16
- 8 → 24 → ×3 → $1 \times 3 = 3$ → 3:24
- 1 → 4 → ×4 → $8 \times 4 = 32$ → 4:32
- 8 → 40 → ×5 → $1 \times 5 = 5$ → 5:40
- 8 → 48 → ×6 → $1 \times 6 = 6$ → 6:48
✔ Answer:
1 : 8 = 2 : 16 = 3 : 24 = 4 : 32 = 5 : 40 = 6 : 48
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Original: 3:1
- 1 → 2 → ×2 → $3 \times 2 = 6$ → 6:2
- 1 → 3 → ×3 → $3 \times 3 = 9$ → 9:3
- 3 → 12 → ×4 → $1 \times 4 = 4$ → 12:4
- 3 → 15 → ×5 → $1 \times 5 = 5$ → 15:5
- 1 → 6 → ×6 → $3 \times 6 = 18$ → 18:6
✔ Answer:
3 : 1 = 6 : 2 = 9 : 3 = 12 : 4 = 15 : 5 = 18 : 6
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(1) 1 : 2 = 2 : 4 = 3 : 6 = 4 : 8 = 5 : 10 = 6 : 12
(2) 1 : 3 = 2 : 6 = 3 : 9 = 4 : 12 = 5 : 15 = 6 : 18
(3) 1 : 7 = 2 : 14 = 3 : 21 = 4 : 28 = 5 : 35 = 6 : 42
(4) 2 : 5 = 4 : 10 = 6 : 15 = 8 : 20 = 10 : 25 = 12 : 30
(5) 2 : 4 = 4 : 8 = 6 : 12 = 8 : 16 = 10 : 20 = 12 : 24
(6) 5 : 9 = 10 : 18 = 15 : 27 = 20 : 36 = 25 : 45 = 30 : 54
(7) 1 : 5 = 2 : 10 = 3 : 15 = 4 : 20 = 5 : 25 = 6 : 30
(8) 3 : 2 = 6 : 4 = 9 : 6 = 12 : 8 = 15 : 10 = 18 : 12
(9) 1 : 8 = 2 : 16 = 3 : 24 = 4 : 32 = 5 : 40 = 6 : 48
(10) 3 : 1 = 6 : 2 = 9 : 3 = 12 : 4 = 15 : 5 = 18 : 6
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Let me know if you'd like this as a printable PDF or need explanations for any specific part!
We'll use the concept of equivalent ratios, which means multiplying or dividing both terms of the ratio by the same number.
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(1) 1 : 2 = ___ : 4 = ___ : 6 = 4 : ___ = ___ : 10 = 6 : ___
Start with 1:2
- To get from 2 to 4 → multiply by 2 → $1 \times 2 = 2$ → 2:4
- To get from 2 to 6 → multiply by 3 → $1 \times 3 = 3$ → 3:6
- From 1 to 4 → multiply by 4 → $2 \times 4 = 8$ → 4:8
- From 2 to 10 → multiply by 5 → $1 \times 5 = 5$ → 5:10
- From 1 to 6 → multiply by 6 → $2 \times 6 = 12$ → 6:12
✔ Answer:
1 : 2 = 2 : 4 = 3 : 6 = 4 : 8 = 5 : 10 = 6 : 12
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(2) 1 : 3 = ___ : 6 = 3 : ___ = ___ : 12 = 5 : ___ = 6 : ___
Original: 1:3
- 3 → 6 → ×2 → $1 \times 2 = 2$ → 2:6
- 1 → 3 → ×3 → $3 \times 3 = 9$ → 3:9
- 3 → 12 → ×4 → $1 \times 4 = 4$ → 4:12
- 1 → 5 → ×5 → $3 \times 5 = 15$ → 5:15
- 1 → 6 → ×6 → $3 \times 6 = 18$ → 6:18
✔ Answer:
1 : 3 = 2 : 6 = 3 : 9 = 4 : 12 = 5 : 15 = 6 : 18
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(3) 1 : 7 = ___ : 14 = ___ : 21 = 4 : ___ = 5 : ___ = ___ : 42
Original: 1:7
- 7 → 14 → ×2 → $1 \times 2 = 2$ → 2:14
- 7 → 21 → ×3 → $1 \times 3 = 3$ → 3:21
- 1 → 4 → ×4 → $7 \times 4 = 28$ → 4:28
- 1 → 5 → ×5 → $7 \times 5 = 35$ → 5:35
- 7 → 42 → ×6 → $1 \times 6 = 6$ → 6:42
✔ Answer:
1 : 7 = 2 : 14 = 3 : 21 = 4 : 28 = 5 : 35 = 6 : 42
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(4) 2 : 5 = ___ : 10 = ___ : 15 = 8 : ___ = ___ : 25 = ___ : 30
Original: 2:5
- 5 → 10 → ×2 → $2 \times 2 = 4$ → 4:10
- 5 → 15 → ×3 → $2 \times 3 = 6$ → 6:15
- 2 → 8 → ×4 → $5 \times 4 = 20$ → 8:20
- 5 → 25 → ×5 → $2 \times 5 = 10$ → 10:25
- 5 → 30 → ×6 → $2 \times 6 = 12$ → 12:30
✔ Answer:
2 : 5 = 4 : 10 = 6 : 15 = 8 : 20 = 10 : 25 = 12 : 30
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(5) 2 : 4 = ___ : 8 = ___ : 12 = 8 : ___ = ___ : 20 = 12 : ___
Simplify 2:4 → 1:2
But we can work directly:
- 4 → 8 → ×2 → $2 \times 2 = 4$ → 4:8
- 4 → 12 → ×3 → $2 \times 3 = 6$ → 6:12
- 2 → 8 → ×4 → $4 \times 4 = 16$ → 8:16
- 4 → 20 → ×5 → $2 \times 5 = 10$ → 10:20
- 2 → 12 → ×6 → $4 \times 6 = 24$ → 12:24
✔ Answer:
2 : 4 = 4 : 8 = 6 : 12 = 8 : 16 = 10 : 20 = 12 : 24
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(6) 5 : 9 = 10 : ___ = 15 : ___ = 20 : ___ = 25 : ___ = ___ : 54
Original: 5:9
- 5 → 10 → ×2 → $9 \times 2 = 18$ → 10:18
- 5 → 15 → ×3 → $9 \times 3 = 27$ → 15:27
- 5 → 20 → ×4 → $9 \times 4 = 36$ → 20:36
- 5 → 25 → ×5 → $9 \times 5 = 45$ → 25:45
- 9 → 54 → ×6 → $5 \times 6 = 30$ → 30:54
✔ Answer:
5 : 9 = 10 : 18 = 15 : 27 = 20 : 36 = 25 : 45 = 30 : 54
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(7) 1 : 5 = ___ : 10 = 3 : ___ = 4 : ___ = 5 : ___ = 6 : ___
Original: 1:5
- 5 → 10 → ×2 → $1 \times 2 = 2$ → 2:10
- 1 → 3 → ×3 → $5 \times 3 = 15$ → 3:15
- 1 → 4 → ×4 → $5 \times 4 = 20$ → 4:20
- 1 → 5 → ×5 → $5 \times 5 = 25$ → 5:25
- 1 → 6 → ×6 → $5 \times 6 = 30$ → 6:30
✔ Answer:
1 : 5 = 2 : 10 = 3 : 15 = 4 : 20 = 5 : 25 = 6 : 30
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(8) 3 : 2 = ___ : 4 = ___ : 6 = 12 : ___ = ___ : 10 = 18 : ___
Original: 3:2
- 2 → 4 → ×2 → $3 \times 2 = 6$ → 6:4
- 2 → 6 → ×3 → $3 \times 3 = 9$ → 9:6
- 3 → 12 → ×4 → $2 \times 4 = 8$ → 12:8
- 2 → 10 → ×5 → $3 \times 5 = 15$ → 15:10
- 3 → 18 → ×6 → $2 \times 6 = 12$ → 18:12
✔ Answer:
3 : 2 = 6 : 4 = 9 : 6 = 12 : 8 = 15 : 10 = 18 : 12
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(9) 1 : 8 = ___ : 16 = ___ : 24 = 4 : ___ = ___ : 40 = ___ : 48
Original: 1:8
- 8 → 16 → ×2 → $1 \times 2 = 2$ → 2:16
- 8 → 24 → ×3 → $1 \times 3 = 3$ → 3:24
- 1 → 4 → ×4 → $8 \times 4 = 32$ → 4:32
- 8 → 40 → ×5 → $1 \times 5 = 5$ → 5:40
- 8 → 48 → ×6 → $1 \times 6 = 6$ → 6:48
✔ Answer:
1 : 8 = 2 : 16 = 3 : 24 = 4 : 32 = 5 : 40 = 6 : 48
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(10) 3 : 1 = ___ : 2 = ___ : 3 = 12 : ___ = 15 : ___ = ___ : 6
Original: 3:1
- 1 → 2 → ×2 → $3 \times 2 = 6$ → 6:2
- 1 → 3 → ×3 → $3 \times 3 = 9$ → 9:3
- 3 → 12 → ×4 → $1 \times 4 = 4$ → 12:4
- 3 → 15 → ×5 → $1 \times 5 = 5$ → 15:5
- 1 → 6 → ×6 → $3 \times 6 = 18$ → 18:6
✔ Answer:
3 : 1 = 6 : 2 = 9 : 3 = 12 : 4 = 15 : 5 = 18 : 6
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✔ Final Answers Summary:
(1) 1 : 2 = 2 : 4 = 3 : 6 = 4 : 8 = 5 : 10 = 6 : 12
(2) 1 : 3 = 2 : 6 = 3 : 9 = 4 : 12 = 5 : 15 = 6 : 18
(3) 1 : 7 = 2 : 14 = 3 : 21 = 4 : 28 = 5 : 35 = 6 : 42
(4) 2 : 5 = 4 : 10 = 6 : 15 = 8 : 20 = 10 : 25 = 12 : 30
(5) 2 : 4 = 4 : 8 = 6 : 12 = 8 : 16 = 10 : 20 = 12 : 24
(6) 5 : 9 = 10 : 18 = 15 : 27 = 20 : 36 = 25 : 45 = 30 : 54
(7) 1 : 5 = 2 : 10 = 3 : 15 = 4 : 20 = 5 : 25 = 6 : 30
(8) 3 : 2 = 6 : 4 = 9 : 6 = 12 : 8 = 15 : 10 = 18 : 12
(9) 1 : 8 = 2 : 16 = 3 : 24 = 4 : 32 = 5 : 40 = 6 : 48
(10) 3 : 1 = 6 : 2 = 9 : 3 = 12 : 4 = 15 : 5 = 18 : 6
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Let me know if you'd like this as a printable PDF or need explanations for any specific part!
Parent Tip: Review the logic above to help your child master the concept of printable ratio worksheet.
