Equivalent Ratios worksheet for math practice.
Worksheet titled "Equivalent Ratios" with ten problems requiring students to fill in missing values in equivalent ratio equations.
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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 problem step by step.
We’re working with equivalent ratios. That means we multiply or divide both parts of the ratio by the same number to get new ratios that are equal.
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Problem 1: 1 : 7 = __ : 14 = __ : 21 = 4 : __ = 5 : __ = __ : 42
- To get from 7 to 14 → ×2 → so 1×2 = 2
- To get from 7 to 21 → ×3 → so 1×3 = 3
- To get from 1 to 4 → ×4 → so 7×4 = 28
- To get from 1 to 5 → ×5 → so 7×5 = 35
- To get from 7 to 42 → ×6 → so 1×6 = 6
✔ Answer: 2, 3, 28, 35, 6
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Problem 2: 1 : 2 = __ : 4 = 3 : __ = 4 : __ = 5 : __ = 6 : __
- 2 → 4 → ×2 → 1×2 = 2
- 1 → 3 → ×3 → 2×3 = 6
- 1 → 4 → ×4 → 2×4 = 8
- 1 → 5 → ×5 → 2×5 = 10
- 1 → 6 → ×6 → 2×6 = 12
✔ Answer: 2, 6, 8, 10, 12
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Problem 3: 1 : 3 = __ : 6 = 3 : __ = __ : 12 = 5 : __ = 6 : __
- 3 → 6 → ×2 → 1×2 = 2
- 1 → 3 → ×3 → 3×3 = 9
- 3 → 12 → ×4 → 1×4 = 4
- 1 → 5 → ×5 → 3×5 = 15
- 1 → 6 → ×6 → 3×6 = 18
✔ Answer: 2, 9, 4, 15, 18
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Problem 4: 1 : 2 = __ : 4 = __ : 6 = __ : 8 = __ : 10 = 6 : __
- 2 → 4 → ×2 → 1×2 = 2
- 2 → 6 → ×3 → 1×3 = 3
- 2 → 8 → ×4 → 1×4 = 4
- 2 → 10 → ×5 → 1×5 = 5
- 1 → 6 → ×6 → 2×6 = 12
✔ Answer: 2, 3, 4, 5, 12
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Problem 5: 1 : 8 = __ : 16 = __ : 24 = 4 : __ = __ : 40 = __ : 48
- 8 → 16 → ×2 → 1×2 = 2
- 8 → 24 → ×3 → 1×3 = 3
- 1 → 4 → ×4 → 8×4 = 32
- 8 → 40 → ×5 → 1×5 = 5
- 8 → 48 → ×6 → 1×6 = 6
✔ Answer: 2, 3, 32, 5, 6
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Problem 6: 2 : 5 = __ : 10 = __ : 15 = 8 : __ = __ : 25 = __ : 30
- 5 → 10 → ×2 → 2×2 = 4
- 5 → 15 → ×3 → 2×3 = 6
- 2 → 8 → ×4 → 5×4 = 20
- 5 → 25 → ×5 → 2×5 = 10
- 5 → 30 → ×6 → 2×6 = 12
✔ Answer: 4, 6, 20, 10, 12
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Problem 7: 5 : 9 = 10 : __ = 15 : __ = 20 : __ = 25 : __ = __ : 54
- 5 → 10 → ×2 → 9×2 = 18
- 5 → 15 → ×3 → 9×3 = 27
- 5 → 20 → ×4 → 9×4 = 36
- 5 → 25 → ×5 → 9×5 = 45
- 9 → 54 → ×6 → 5×6 = 30
✔ Answer: 18, 27, 36, 45, 30
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Problem 8: 1 : 2 = __ : 4 = __ : 6 = 4 : __ = __ : 10 = 6 : __
- 2 → 4 → ×2 → 1×2 = 2
- 2 → 6 → ×3 → 1×3 = 3
- 1 → 4 → ×4 → 2×4 = 8
- 1 → 5? Wait — let’s check: 2 → 10 → ×5 → 1×5 = 5
- 1 → 6 → ×6 → 2×6 = 12
Wait — in problem 8, it says “__ : 10” and “6 : __”
So:
- For __ : 10 → since second part is 10, and original is 2 → ×5 → first part 1×5 = 5
- For 6 : __ → first part 6 → 1×6 → second part 2×6 = 12
✔ Answer: 2, 3, 8, 5, 12
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Problem 9: 1 : 2 = 2 : __ = __ : 6 = 4 : __ = __ : 10 = __ : 12
- 1 → 2 → ×2 → 2×2 = 4
- 1 → ? for __ : 6 → 2→6 → ×3 → 1×3 = 3
- 1 → 4 → ×4 → 2×4 = 8
- 1 → ? for __ : 10 → 2→10 → ×5 → 1×5 = 5
- 1 → ? for __ : 12 → 2→12 → ×6 → 1×6 = 6
✔ Answer: 4, 3, 8, 5, 6
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Problem 10: 1 : 3 = __ : 6 = __ : 9 = 4 : __ = __ : 15 = __ : 18
- 3 → 6 → ×2 → 1×2 = 2
- 3 → 9 → ×3 → 1×3 = 3
- 1 → 4 → ×4 → 3×4 = 12
- 3 → 15 → ×5 → 1×5 = 5
- 3 → 18 → ×6 → 1×6 = 6
✔ Answer: 2, 3, 12, 5, 6
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Final Answer:
1) 2, 3, 28, 35, 6
2) 2, 6, 8, 10, 12
3) 2, 9, 4, 15, 18
4) 2, 3, 4, 5, 12
5) 2, 3, 32, 5, 6
6) 4, 6, 20, 10, 12
7) 18, 27, 36, 45, 30
8) 2, 3, 8, 5, 12
9) 4, 3, 8, 5, 6
10) 2, 3, 12, 5, 6
We’re working with equivalent ratios. That means we multiply or divide both parts of the ratio by the same number to get new ratios that are equal.
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Problem 1: 1 : 7 = __ : 14 = __ : 21 = 4 : __ = 5 : __ = __ : 42
- To get from 7 to 14 → ×2 → so 1×2 = 2
- To get from 7 to 21 → ×3 → so 1×3 = 3
- To get from 1 to 4 → ×4 → so 7×4 = 28
- To get from 1 to 5 → ×5 → so 7×5 = 35
- To get from 7 to 42 → ×6 → so 1×6 = 6
✔ Answer: 2, 3, 28, 35, 6
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Problem 2: 1 : 2 = __ : 4 = 3 : __ = 4 : __ = 5 : __ = 6 : __
- 2 → 4 → ×2 → 1×2 = 2
- 1 → 3 → ×3 → 2×3 = 6
- 1 → 4 → ×4 → 2×4 = 8
- 1 → 5 → ×5 → 2×5 = 10
- 1 → 6 → ×6 → 2×6 = 12
✔ Answer: 2, 6, 8, 10, 12
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Problem 3: 1 : 3 = __ : 6 = 3 : __ = __ : 12 = 5 : __ = 6 : __
- 3 → 6 → ×2 → 1×2 = 2
- 1 → 3 → ×3 → 3×3 = 9
- 3 → 12 → ×4 → 1×4 = 4
- 1 → 5 → ×5 → 3×5 = 15
- 1 → 6 → ×6 → 3×6 = 18
✔ Answer: 2, 9, 4, 15, 18
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Problem 4: 1 : 2 = __ : 4 = __ : 6 = __ : 8 = __ : 10 = 6 : __
- 2 → 4 → ×2 → 1×2 = 2
- 2 → 6 → ×3 → 1×3 = 3
- 2 → 8 → ×4 → 1×4 = 4
- 2 → 10 → ×5 → 1×5 = 5
- 1 → 6 → ×6 → 2×6 = 12
✔ Answer: 2, 3, 4, 5, 12
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Problem 5: 1 : 8 = __ : 16 = __ : 24 = 4 : __ = __ : 40 = __ : 48
- 8 → 16 → ×2 → 1×2 = 2
- 8 → 24 → ×3 → 1×3 = 3
- 1 → 4 → ×4 → 8×4 = 32
- 8 → 40 → ×5 → 1×5 = 5
- 8 → 48 → ×6 → 1×6 = 6
✔ Answer: 2, 3, 32, 5, 6
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Problem 6: 2 : 5 = __ : 10 = __ : 15 = 8 : __ = __ : 25 = __ : 30
- 5 → 10 → ×2 → 2×2 = 4
- 5 → 15 → ×3 → 2×3 = 6
- 2 → 8 → ×4 → 5×4 = 20
- 5 → 25 → ×5 → 2×5 = 10
- 5 → 30 → ×6 → 2×6 = 12
✔ Answer: 4, 6, 20, 10, 12
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Problem 7: 5 : 9 = 10 : __ = 15 : __ = 20 : __ = 25 : __ = __ : 54
- 5 → 10 → ×2 → 9×2 = 18
- 5 → 15 → ×3 → 9×3 = 27
- 5 → 20 → ×4 → 9×4 = 36
- 5 → 25 → ×5 → 9×5 = 45
- 9 → 54 → ×6 → 5×6 = 30
✔ Answer: 18, 27, 36, 45, 30
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Problem 8: 1 : 2 = __ : 4 = __ : 6 = 4 : __ = __ : 10 = 6 : __
- 2 → 4 → ×2 → 1×2 = 2
- 2 → 6 → ×3 → 1×3 = 3
- 1 → 4 → ×4 → 2×4 = 8
- 1 → 5? Wait — let’s check: 2 → 10 → ×5 → 1×5 = 5
- 1 → 6 → ×6 → 2×6 = 12
Wait — in problem 8, it says “__ : 10” and “6 : __”
So:
- For __ : 10 → since second part is 10, and original is 2 → ×5 → first part 1×5 = 5
- For 6 : __ → first part 6 → 1×6 → second part 2×6 = 12
✔ Answer: 2, 3, 8, 5, 12
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Problem 9: 1 : 2 = 2 : __ = __ : 6 = 4 : __ = __ : 10 = __ : 12
- 1 → 2 → ×2 → 2×2 = 4
- 1 → ? for __ : 6 → 2→6 → ×3 → 1×3 = 3
- 1 → 4 → ×4 → 2×4 = 8
- 1 → ? for __ : 10 → 2→10 → ×5 → 1×5 = 5
- 1 → ? for __ : 12 → 2→12 → ×6 → 1×6 = 6
✔ Answer: 4, 3, 8, 5, 6
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Problem 10: 1 : 3 = __ : 6 = __ : 9 = 4 : __ = __ : 15 = __ : 18
- 3 → 6 → ×2 → 1×2 = 2
- 3 → 9 → ×3 → 1×3 = 3
- 1 → 4 → ×4 → 3×4 = 12
- 3 → 15 → ×5 → 1×5 = 5
- 3 → 18 → ×6 → 1×6 = 6
✔ Answer: 2, 3, 12, 5, 6
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Final Answer:
1) 2, 3, 28, 35, 6
2) 2, 6, 8, 10, 12
3) 2, 9, 4, 15, 18
4) 2, 3, 4, 5, 12
5) 2, 3, 32, 5, 6
6) 4, 6, 20, 10, 12
7) 18, 27, 36, 45, 30
8) 2, 3, 8, 5, 12
9) 4, 3, 8, 5, 6
10) 2, 3, 12, 5, 6
Parent Tip: Review the logic above to help your child master the concept of ratios 6th grade worksheet.
