Equivalent ratios - Ratio and Proportion by URBrainy.com - Free Printable

Let's solve this equivalent ratios worksheet step by step. The goal is to fill in the missing numbers so that each ratio is equivalent to the original one.

We'll go through each question and explain how to find the missing numbers using multiplication or division to maintain the same ratio.

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🔹 1. 1 : 6 = 2 : 12 = ... : 18 = ... : 24 = 5 : ... = ... : 36

We start with 1:6.

- Multiply both sides by 3 → 1×3 : 6×3 = 3 : 18
- Multiply by 4 → 1×4 : 6×4 = 4 : 24
- Multiply by 5 → 1×5 : 6×5 = 5 : 30
- Multiply by 6 → 1×6 : 6×6 = 6 : 36

✔ So, the full row is:
> 1 : 6 = 2 : 12 = 3 : 18 = 4 : 24 = 5 : 30 = 6 : 36

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🔹 2. 3 : 10 = ... : 20 = ... : 30 = 12 : ... = 15 : ... = 18 : ...

Start with 3:10

- To get from 10 to 20 → ×2 → 3×2 = 6, so 6 : 20
- From 10 to 30 → ×3 → 3×3 = 9, so 9 : 30
- From 3 to 12 → ×4 → 10×4 = 40, so 12 : 40
- From 3 to 15 → ×5 → 10×5 = 50, so 15 : 50
- From 3 to 18 → ×6 → 10×6 = 60, so 18 : 60

✔ So:
> 3 : 10 = 6 : 20 = 9 : 30 = 12 : 40 = 15 : 50 = 18 : 60

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🔹 3. 3 : 8 = ... : 16 = ... : 24 = 12 : ... = 15 : ... = 18 : ...

Start with 3:8

- 8 → 16 → ×2 → 3×2 = 6, so 6 : 16
- 8 → 24 → ×3 → 3×3 = 9, so 9 : 24
- 3 → 12 → ×4 → 8×4 = 32, so 12 : 32
- 3 → 15 → ×5 → 8×5 = 40, so 15 : 40
- 3 → 18 → ×6 → 8×6 = 48, so 18 : 48

✔ So:
> 3 : 8 = 6 : 16 = 9 : 24 = 12 : 32 = 15 : 40 = 18 : 48

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🔹 4. 1 : 9 = ... : 18 = ... : 27 = 4 : ... = ... : 45 = 6 : ...

Start with 1:9

- 9 → 18 → ×2 → 1×2 = 2, so 2 : 18
- 9 → 27 → ×3 → 1×3 = 3, so 3 : 27
- 1 → 4 → ×4 → 9×4 = 36, so 4 : 36
- 9 → 45 → ×5 → 1×5 = 5, so 5 : 45
- 1 → 6 → ×6 → 9×6 = 54, so 6 : 54

✔ So:
> 1 : 9 = 2 : 18 = 3 : 27 = 4 : 36 = 5 : 45 = 6 : 54

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🔹 5. 2 : 5 = 4 : ... = ... : 15 = ... : 20 = ... : 25 = ... : 30

Start with 2:5

- 2 → 4 → ×2 → 5×2 = 10, so 4 : 10
- 5 → 15 → ×3 → 2×3 = 6, so 6 : 15
- 5 → 20 → ×4 → 2×4 = 8, so 8 : 20
- 5 → 25 → ×5 → 2×5 = 10, so 10 : 25
- 5 → 30 → ×6 → 2×6 = 12, so 12 : 30

✔ So:
> 2 : 5 = 4 : 10 = 6 : 15 = 8 : 20 = 10 : 25 = 12 : 30

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Now we move to the "a little bit harder" section.

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🔹 6. 6 : 18 = 5 : ... = 2 : ... = 3 : ... = 4 : ... = ... : 3

First simplify 6:18 → divide both by 6 → 1:3

So all ratios must be equivalent to 1:3

Now:
- 5 : ? → 5×3 = 15, so 5 : 15
- 2 : ? → 2×3 = 6, so 2 : 6
- 3 : ? → 3×3 = 9, so 3 : 9
- 4 : ? → 4×3 = 12, so 4 : 12
- ? : 3 → since it's 1:3, then 1×3 = 3 → so 1 : 3

✔ So:
> 6 : 18 = 5 : 15 = 2 : 6 = 3 : 9 = 4 : 12 = 1 : 3

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🔹 7. 18 : 24 = 15 : ... = ... : 8 = 9 : ... = ... : 16 = 3 : ...

Simplify 18:24 → divide by 6 → 3:4

So all ratios must be equivalent to 3:4

Now:
- 15 : ? → 15 ÷ 3 = 5 → 4×5 = 20, so 15 : 20
- ? : 8 → 8 ÷ 4 = 2 → 3×2 = 6, so 6 : 8
- 9 : ? → 9 ÷ 3 = 3 → 4×3 = 12, so 9 : 12
- ? : 16 → 16 ÷ 4 = 4 → 3×4 = 12, so 12 : 16
- 3 : ? → 3×4 = 12, so 3 : 12

✔ So:
> 18 : 24 = 15 : 20 = 6 : 8 = 9 : 12 = 12 : 16 = 3 : 12

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🔹 8. 30 : 36 = ... : 30 = 10 : ... = ... : 18 = 20 : ... = ... : 6

Simplify 30:36 → divide by 6 → 5:6

So all ratios are 5:6

Now:
- ? : 30 → 30 ÷ 6 = 5 → 5×5 = 25, so 25 : 30
- 10 : ? → 10 ÷ 5 = 2 → 6×2 = 12, so 10 : 12
- ? : 18 → 18 ÷ 6 = 3 → 5×3 = 15, so 15 : 18
- 20 : ? → 20 ÷ 5 = 4 → 6×4 = 24, so 20 : 24
- ? : 6 → 6 ÷ 6 = 1 → 5×1 = 5, so 5 : 6

✔ So:
> 30 : 36 = 25 : 30 = 10 : 12 = 15 : 18 = 20 : 24 = 5 : 6

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🔹 9. 12 : 30 = ... : 25 = 4 : ... = ... : 15 = ... : 20 = 2 : ...

Simplify 12:30 → divide by 6 → 2:5

So all ratios are 2:5

Now:
- ? : 25 → 25 ÷ 5 = 5 → 2×5 = 10, so 10 : 25
- 4 : ? → 4 ÷ 2 = 2 → 5×2 = 10, so 4 : 10
- ? : 15 → 15 ÷ 5 = 3 → 2×3 = 6, so 6 : 15
- ? : 20 → 20 ÷ 5 = 4 → 2×4 = 8, so 8 : 20
- 2 : ? → 2×5 = 10, so 2 : 10

✔ So:
> 12 : 30 = 10 : 25 = 4 : 10 = 6 : 15 = 8 : 20 = 2 : 10

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🔹 10. 12 : 18 = ... : 15 = 4 : ... = ... : 9 = ... : 12 = 2 : ...

Simplify 12:18 → divide by 6 → 2:3

So all ratios are 2:3

Now:
- ? : 15 → 15 ÷ 3 = 5 → 2×5 = 10, so 10 : 15
- 4 : ? → 4 ÷ 2 = 2 → 3×2 = 6, so 4 : 6
- ? : 9 → 9 ÷ 3 = 3 → 2×3 = 6, so 6 : 9
- ? : 12 → 12 ÷ 3 = 4 → 2×4 = 8, so 8 : 12
- 2 : ? → 2×3 = 6, so 2 : 6

✔ So:
> 12 : 18 = 10 : 15 = 4 : 6 = 6 : 9 = 8 : 12 = 2 : 6

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✔ Final Answer Summary:

1. 1 : 6 = 2 : 12 = 3 : 18 = 4 : 24 = 5 : 30 = 6 : 36
2. 3 : 10 = 6 : 20 = 9 : 30 = 12 : 40 = 15 : 50 = 18 : 60
3. 3 : 8 = 6 : 16 = 9 : 24 = 12 : 32 = 15 : 40 = 18 : 48
4. 1 : 9 = 2 : 18 = 3 : 27 = 4 : 36 = 5 : 45 = 6 : 54
5. 2 : 5 = 4 : 10 = 6 : 15 = 8 : 20 = 10 : 25 = 12 : 30
6. 6 : 18 = 5 : 15 = 2 : 6 = 3 : 9 = 4 : 12 = 1 : 3
7. 18 : 24 = 15 : 20 = 6 : 8 = 9 : 12 = 12 : 16 = 3 : 12
8. 30 : 36 = 25 : 30 = 10 : 12 = 15 : 18 = 20 : 24 = 5 : 6
9. 12 : 30 = 10 : 25 = 4 : 10 = 6 : 15 = 8 : 20 = 2 : 10
10. 12 : 18 = 10 : 15 = 4 : 6 = 6 : 9 = 8 : 12 = 2 : 6

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💡 Tips for Solving Equivalent Ratios:

- Always simplify the original ratio first (divide both numbers by their GCF).
- Then scale up or down using multiplication or division.
- If one number is given, use cross-multiplication or proportion rules.

Let me know if you'd like a printable version or explanation of any specific step!