Equivalent Ratios worksheet with ten problems for practicing ratio completion.
A worksheet titled "Equivalent Ratios" with ten problems requiring students to fill in missing values in ratio equations. The worksheet includes spaces for name, teacher, score, and date at the top.
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Step-by-step solution for: Ratio Worksheets | Ratio Worksheets for Teachers
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Show Answer Key & Explanations
Step-by-step solution for: Ratio Worksheets | Ratio Worksheets for Teachers
Let's solve each of these equivalent ratios problems step by step.
The idea behind equivalent ratios is that if two ratios are equal, then they can be scaled up or down by multiplying or dividing both terms by the same number.
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We start with 1:7.
- To get from 7 to 14 → multiply by 2 → so 1 × 2 = 2 → 2:14
- 7 to 21 → ×3 → 1×3 = 3 → 3:21
- 4 : ? → We know 1:7 = 4:?, so 1×4 = 4, 7×4 = 28 → 4:28
- 5 : ? → 1×5 = 5, 7×5 = 35 → 5:35
- ? : 42 → 7×6 = 42, so 1×6 = 6 → 6:42
✔ Answer:
1 : 7 = 2 : 14 = 3 : 21 = 4 : 28 = 5 : 35 = 6 : 42
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Start with 1:2
- 2 → 4 → ×2 → 1×2 = 2 → 2:4
- 3 : ? → 1×3 = 3, 2×3 = 6 → 3:6
- 4 : ? → 2×2 = 4 → 2×2 = 8 → 4:8
- 5 : ? → 2×5 = 10 → 5:10
- 6 : ? → 2×6 = 12 → 6:12
✔ Answer:
1 : 2 = 2 : 4 = 3 : 6 = 4 : 8 = 5 : 10 = 6 : 12
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1:3
- 3 → 6 → ×2 → 1×2 = 2 → 2:6
- 3 : ? → 1×3 = 3, 3×3 = 9 → 3:9
- ? : 12 → 3×4 = 12 → 1×4 = 4 → 4:12
- 5 : ? → 3×5 = 15 → 5:15
- 6 : ? → 3×6 = 18 → 6:18
✔ Answer:
1 : 3 = 2 : 6 = 3 : 9 = 4 : 12 = 5 : 15 = 6 : 18
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1:2
- 2 → 4 → ×2 → 1×2 = 2 → 2:4
- 2 → 6 → ×3 → 1×3 = 3 → 3:6
- 2 → 8 → ×4 → 1×4 = 4 → 4:8
- 2 → 10 → ×5 → 1×5 = 5 → 5:10
- 6 : ? → 1→6 → ×6 → 2×6 = 12 → 6:12
✔ Answer:
1 : 2 = 2 : 4 = 3 : 6 = 4 : 8 = 5 : 10 = 6 : 12
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1:8
- 8 → 16 → ×2 → 1×2 = 2 → 2:16
- 8 → 24 → ×3 → 1×3 = 3 → 3:24
- 4 : ? → 1→4 → ×4 → 8×4 = 32 → 4:32
- ? : 40 → 8×5 = 40 → 1×5 = 5 → 5:40
- ? : 48 → 8×6 = 48 → 1×6 = 6 → 6:48
✔ Answer:
1 : 8 = 2 : 16 = 3 : 24 = 4 : 32 = 5 : 40 = 6 : 48
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2:5
- 5 → 10 → ×2 → 2×2 = 4 → 4:10
- 5 → 15 → ×3 → 2×3 = 6 → 6:15
- 8 : ? → 2→8 → ×4 → 5×4 = 20 → 8:20
- ? : 25 → 5×5 = 25 → 2×5 = 10 → 10:25
- ? : 30 → 5×6 = 30 → 2×6 = 12 → 12:30
✔ Answer:
2 : 5 = 4 : 10 = 6 : 15 = 8 : 20 = 10 : 25 = 12 : 30
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5:9
- 5 → 10 → ×2 → 9×2 = 18 → 10:18
- 5 → 15 → ×3 → 9×3 = 27 → 15:27
- 5 → 20 → ×4 → 9×4 = 36 → 20:36
- 5 → 25 → ×5 → 9×5 = 45 → 25:45
- ? : 54 → 9×6 = 54 → 5×6 = 30 → 30:54
✔ Answer:
5 : 9 = 10 : 18 = 15 : 27 = 20 : 36 = 25 : 45 = 30 : 54
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1:2
- 2 → 4 → ×2 → 1×2 = 2 → 2:4
- 2 → 6 → ×3 → 1×3 = 3 → 3:6
- 4 : ? → 1→4 → ×4 → 2×4 = 8 → 4:8
- ? : 10 → 2×5 = 10 → 1×5 = 5 → 5:10
- 6 : ? → 1→6 → ×6 → 2×6 = 12 → 6:12
✔ Answer:
1 : 2 = 2 : 4 = 3 : 6 = 4 : 8 = 5 : 10 = 6 : 12
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1:2
- 2 : ? → 1→2 → ×2 → 2×2 = 4 → 2:4
- ? : 6 → 2×3 = 6 → 1×3 = 3 → 3:6
- 4 : ? → 1→4 → ×4 → 2×4 = 8 → 4:8
- ? : 10 → 2×5 = 10 → 1×5 = 5 → 5:10
- ? : 12 → 2×6 = 12 → 1×6 = 6 → 6:12
✔ Answer:
1 : 2 = 2 : 4 = 3 : 6 = 4 : 8 = 5 : 10 = 6 : 12
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1:3
- 3 → 6 → ×2 → 1×2 = 2 → 2:6
- 3 → 9 → ×3 → 1×3 = 3 → 3:9
- 4 : ? → 1→4 → ×4 → 3×4 = 12 → 4:12
- ? : 15 → 3×5 = 15 → 1×5 = 5 → 5:15
- ? : 18 → 3×6 = 18 → 1×6 = 6 → 6:18
✔ Answer:
1 : 3 = 2 : 6 = 3 : 9 = 4 : 12 = 5 : 15 = 6 : 18
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1) 1 : 7 = 2 : 14 = 3 : 21 = 4 : 28 = 5 : 35 = 6 : 42
2) 1 : 2 = 2 : 4 = 3 : 6 = 4 : 8 = 5 : 10 = 6 : 12
3) 1 : 3 = 2 : 6 = 3 : 9 = 4 : 12 = 5 : 15 = 6 : 18
4) 1 : 2 = 2 : 4 = 3 : 6 = 4 : 8 = 5 : 10 = 6 : 12
5) 1 : 8 = 2 : 16 = 3 : 24 = 4 : 32 = 5 : 40 = 6 : 48
6) 2 : 5 = 4 : 10 = 6 : 15 = 8 : 20 = 10 : 25 = 12 : 30
7) 5 : 9 = 10 : 18 = 15 : 27 = 20 : 36 = 25 : 45 = 30 : 54
8) 1 : 2 = 2 : 4 = 3 : 6 = 4 : 8 = 5 : 10 = 6 : 12
9) 1 : 2 = 2 : 4 = 3 : 6 = 4 : 8 = 5 : 10 = 6 : 12
10) 1 : 3 = 2 : 6 = 3 : 9 = 4 : 12 = 5 : 15 = 6 : 18
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✔ All solved! Each ratio maintains the same proportion by scaling both parts equally. Let me know if you'd like a printable version or explanation in another format!
The idea behind equivalent ratios is that if two ratios are equal, then they can be scaled up or down by multiplying or dividing both terms by the same number.
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1) 1 : 7 = __ : 14 = __ : 21 = 4 : __ = 5 : __ = __ : 42
We start with 1:7.
- To get from 7 to 14 → multiply by 2 → so 1 × 2 = 2 → 2:14
- 7 to 21 → ×3 → 1×3 = 3 → 3:21
- 4 : ? → We know 1:7 = 4:?, so 1×4 = 4, 7×4 = 28 → 4:28
- 5 : ? → 1×5 = 5, 7×5 = 35 → 5:35
- ? : 42 → 7×6 = 42, so 1×6 = 6 → 6:42
✔ Answer:
1 : 7 = 2 : 14 = 3 : 21 = 4 : 28 = 5 : 35 = 6 : 42
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2) 1 : 2 = __ : 4 = 3 : __ = 4 : __ = 5 : __ = 6 : __
Start with 1:2
- 2 → 4 → ×2 → 1×2 = 2 → 2:4
- 3 : ? → 1×3 = 3, 2×3 = 6 → 3:6
- 4 : ? → 2×2 = 4 → 2×2 = 8 → 4:8
- 5 : ? → 2×5 = 10 → 5:10
- 6 : ? → 2×6 = 12 → 6:12
✔ Answer:
1 : 2 = 2 : 4 = 3 : 6 = 4 : 8 = 5 : 10 = 6 : 12
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3) 1 : 3 = __ : 6 = 3 : __ = __ : 12 = 5 : __ = 6 : __
1:3
- 3 → 6 → ×2 → 1×2 = 2 → 2:6
- 3 : ? → 1×3 = 3, 3×3 = 9 → 3:9
- ? : 12 → 3×4 = 12 → 1×4 = 4 → 4:12
- 5 : ? → 3×5 = 15 → 5:15
- 6 : ? → 3×6 = 18 → 6:18
✔ Answer:
1 : 3 = 2 : 6 = 3 : 9 = 4 : 12 = 5 : 15 = 6 : 18
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4) 1 : 2 = __ : 4 = __ : 6 = __ : 8 = __ : 10 = 6 : __
1:2
- 2 → 4 → ×2 → 1×2 = 2 → 2:4
- 2 → 6 → ×3 → 1×3 = 3 → 3:6
- 2 → 8 → ×4 → 1×4 = 4 → 4:8
- 2 → 10 → ×5 → 1×5 = 5 → 5:10
- 6 : ? → 1→6 → ×6 → 2×6 = 12 → 6:12
✔ Answer:
1 : 2 = 2 : 4 = 3 : 6 = 4 : 8 = 5 : 10 = 6 : 12
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5) 1 : 8 = __ : 16 = __ : 24 = 4 : __ = __ : 40 = __ : 48
1:8
- 8 → 16 → ×2 → 1×2 = 2 → 2:16
- 8 → 24 → ×3 → 1×3 = 3 → 3:24
- 4 : ? → 1→4 → ×4 → 8×4 = 32 → 4:32
- ? : 40 → 8×5 = 40 → 1×5 = 5 → 5:40
- ? : 48 → 8×6 = 48 → 1×6 = 6 → 6:48
✔ Answer:
1 : 8 = 2 : 16 = 3 : 24 = 4 : 32 = 5 : 40 = 6 : 48
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6) 2 : 5 = __ : 10 = __ : 15 = 8 : __ = __ : 25 = __ : 30
2:5
- 5 → 10 → ×2 → 2×2 = 4 → 4:10
- 5 → 15 → ×3 → 2×3 = 6 → 6:15
- 8 : ? → 2→8 → ×4 → 5×4 = 20 → 8:20
- ? : 25 → 5×5 = 25 → 2×5 = 10 → 10:25
- ? : 30 → 5×6 = 30 → 2×6 = 12 → 12:30
✔ Answer:
2 : 5 = 4 : 10 = 6 : 15 = 8 : 20 = 10 : 25 = 12 : 30
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7) 5 : 9 = 10 : __ = 15 : __ = 20 : __ = 25 : __ = __ : 54
5:9
- 5 → 10 → ×2 → 9×2 = 18 → 10:18
- 5 → 15 → ×3 → 9×3 = 27 → 15:27
- 5 → 20 → ×4 → 9×4 = 36 → 20:36
- 5 → 25 → ×5 → 9×5 = 45 → 25:45
- ? : 54 → 9×6 = 54 → 5×6 = 30 → 30:54
✔ Answer:
5 : 9 = 10 : 18 = 15 : 27 = 20 : 36 = 25 : 45 = 30 : 54
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8) 1 : 2 = __ : 4 = __ : 6 = 4 : __ = __ : 10 = 6 : __
1:2
- 2 → 4 → ×2 → 1×2 = 2 → 2:4
- 2 → 6 → ×3 → 1×3 = 3 → 3:6
- 4 : ? → 1→4 → ×4 → 2×4 = 8 → 4:8
- ? : 10 → 2×5 = 10 → 1×5 = 5 → 5:10
- 6 : ? → 1→6 → ×6 → 2×6 = 12 → 6:12
✔ Answer:
1 : 2 = 2 : 4 = 3 : 6 = 4 : 8 = 5 : 10 = 6 : 12
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9) 1 : 2 = 2 : __ = __ : 6 = 4 : __ = __ : 10 = __ : 12
1:2
- 2 : ? → 1→2 → ×2 → 2×2 = 4 → 2:4
- ? : 6 → 2×3 = 6 → 1×3 = 3 → 3:6
- 4 : ? → 1→4 → ×4 → 2×4 = 8 → 4:8
- ? : 10 → 2×5 = 10 → 1×5 = 5 → 5:10
- ? : 12 → 2×6 = 12 → 1×6 = 6 → 6:12
✔ Answer:
1 : 2 = 2 : 4 = 3 : 6 = 4 : 8 = 5 : 10 = 6 : 12
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10) 1 : 3 = __ : 6 = __ : 9 = 4 : __ = __ : 15 = __ : 18
1:3
- 3 → 6 → ×2 → 1×2 = 2 → 2:6
- 3 → 9 → ×3 → 1×3 = 3 → 3:9
- 4 : ? → 1→4 → ×4 → 3×4 = 12 → 4:12
- ? : 15 → 3×5 = 15 → 1×5 = 5 → 5:15
- ? : 18 → 3×6 = 18 → 1×6 = 6 → 6:18
✔ Answer:
1 : 3 = 2 : 6 = 3 : 9 = 4 : 12 = 5 : 15 = 6 : 18
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✔ Final Answers:
1) 1 : 7 = 2 : 14 = 3 : 21 = 4 : 28 = 5 : 35 = 6 : 42
2) 1 : 2 = 2 : 4 = 3 : 6 = 4 : 8 = 5 : 10 = 6 : 12
3) 1 : 3 = 2 : 6 = 3 : 9 = 4 : 12 = 5 : 15 = 6 : 18
4) 1 : 2 = 2 : 4 = 3 : 6 = 4 : 8 = 5 : 10 = 6 : 12
5) 1 : 8 = 2 : 16 = 3 : 24 = 4 : 32 = 5 : 40 = 6 : 48
6) 2 : 5 = 4 : 10 = 6 : 15 = 8 : 20 = 10 : 25 = 12 : 30
7) 5 : 9 = 10 : 18 = 15 : 27 = 20 : 36 = 25 : 45 = 30 : 54
8) 1 : 2 = 2 : 4 = 3 : 6 = 4 : 8 = 5 : 10 = 6 : 12
9) 1 : 2 = 2 : 4 = 3 : 6 = 4 : 8 = 5 : 10 = 6 : 12
10) 1 : 3 = 2 : 6 = 3 : 9 = 4 : 12 = 5 : 15 = 6 : 18
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✔ All solved! Each ratio maintains the same proportion by scaling both parts equally. Let me know if you'd like a printable version or explanation in another format!
Parent Tip: Review the logic above to help your child master the concept of math ratio problems.
