Ratio Worksheets - Free Printable

The image you've uploaded is a math worksheet titled "Creating Equivalent Ratios", with 20 problems where students are asked to fill in the blank to make an equivalent ratio. The answer key is already provided on the right side of the page.

Let me walk through how to solve these types of problems and explain the reasoning behind each answer, using the concept of equivalent ratios.

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🔷 What Are Equivalent Ratios?

Two ratios are equivalent if they represent the same relationship between numbers. You can create equivalent ratios by multiplying or dividing both terms of the ratio by the same non-zero number.

For example:
- $ 1:2 = 2:4 = 3:6 $ — all are equivalent because each is obtained by multiplying both parts by the same number.

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✔ How to Solve Each Problem

We'll go step-by-step through the logic for a few examples (and confirm the answers match the key).

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#### 1) 12 : ___ = 16 : 24

We want to find a number such that $ 12 : x = 16 : 24 $

First, simplify $ 16:24 $ → divide both by 8 → $ 2:3 $

Now, we want $ 12 : x = 2 : 3 $

Set up proportion:
$$
\frac{12}{x} = \frac{2}{3}
$$

Cross-multiply:
$ 12 \times 3 = 2x $ → $ 36 = 2x $ → $ x = 18 $

✔ Answer: 18

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#### 2) 18 : 10 = ___ : 5

Simplify $ 18:10 $ → divide by 2 → $ 9:5 $

So $ 18:10 = 9:5 $ → missing number is 9

✔ Answer: 9

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#### 3) 6 : 7 = ___ : 21

We know $ 6:7 = x:21 $

Since 21 is $ 7 \times 3 $, multiply both sides of $ 6:7 $ by 3:

→ $ 6 \times 3 = 18 $, $ 7 \times 3 = 21 $

So $ 6:7 = 18:21 $

✔ Answer: 18

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#### 4) 7 : 1 = ___ : 2

Multiply both sides by 2:
$ 7 \times 2 = 14 $, $ 1 \times 2 = 2 $

So $ 7:1 = 14:2 $

✔ Answer: 14

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#### 5) 8 : 3 = ___ : 27

We see that $ 3 \times 9 = 27 $, so multiply both sides of $ 8:3 $ by 9:

→ $ 8 \times 9 = 72 $, $ 3 \times 9 = 27 $

So $ 8:3 = 72:27 $

✔ Answer: 72

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#### 6) ___ : 32 = 21 : 28

Simplify $ 21:28 $ → divide by 7 → $ 3:4 $

So $ x:32 = 3:4 $

Now, since $ 32 \div 8 = 4 $, then $ x = 3 \times 8 = 24 $

Or set up:
$ \frac{x}{32} = \frac{3}{4} $ → $ x = \frac{3 \times 32}{4} = 24 $

✔ Answer: 24

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#### 7) ___ : 40 = 6 : 24

Simplify $ 6:24 $ → divide by 6 → $ 1:4 $

So $ x:40 = 1:4 $

Since $ 40 \div 4 = 10 $, then $ x = 1 \times 10 = 10 $

✔ Answer: 10

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#### 8) 15 : ___ = 24 : 56

Simplify $ 24:56 $ → divide by 8 → $ 3:7 $

So $ 15:x = 3:7 $

Now, $ 15 \div 3 = 5 $, so multiply $ 3:7 $ by 5 → $ 15:35 $

Thus, $ x = 35 $

✔ Answer: 35

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#### 9) ___ : 5 = 16 : 20

Simplify $ 16:20 $ → divide by 4 → $ 4:5 $

So $ x:5 = 4:5 $ → $ x = 4 $

✔ Answer: 4

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#### 10) 16 : 32 = ___ : 4

Simplify $ 16:32 $ → $ 1:2 $

So $ 1:2 = x:4 $

Since $ 4 \div 2 = 2 $, $ x = 1 \times 2 = 2 $

✔ Answer: 2

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#### 11) ___ : 2 = 28 : 8

Simplify $ 28:8 $ → divide by 4 → $ 7:2 $

So $ x:2 = 7:2 $ → $ x = 7 $

✔ Answer: 7

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#### 12) 7 : 56 = ___ : 72

Simplify $ 7:56 $ → divide by 7 → $ 1:8 $

So $ 1:8 = x:72 $

Since $ 72 \div 8 = 9 $, $ x = 1 \times 9 = 9 $

✔ Answer: 9

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#### 13) 8 : 32 = 1 : ___

Simplify $ 8:32 $ → divide by 8 → $ 1:4 $

So $ 8:32 = 1:4 $

✔ Answer: 4

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#### 14) 5 : 3 = 45 : ___

$ 5 \times 9 = 45 $, so multiply $ 3 \times 9 = 27 $

So $ 5:3 = 45:27 $

✔ Answer: 27

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#### 15) ___ : 20 = 8 : 5

Simplify $ 8:5 $ → already simplified.

We want $ x:20 = 8:5 $

So $ \frac{x}{20} = \frac{8}{5} $ → $ x = \frac{8 \times 20}{5} = 32 $

✔ Answer: 32

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#### 16) 6 : ___ = 2 : 6

Simplify $ 2:6 $ → $ 1:3 $

So $ 6:x = 1:3 $

Since $ 6 \div 1 = 6 $, then $ x = 3 \times 6 = 18 $

✔ Answer: 18

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#### 17) 8 : 24 = 1 : ___

Simplify $ 8:24 $ → divide by 8 → $ 1:3 $

So $ 8:24 = 1:3 $

✔ Answer: 3

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#### 18) 3 : 6 = ___ : 30

Simplify $ 3:6 $ → $ 1:2 $

So $ 1:2 = x:30 $

Since $ 30 \div 2 = 15 $, $ x = 1 \times 15 = 15 $

✔ Answer: 15

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#### 19) ___ : 15 = 6 : 5

Set up: $ x:15 = 6:5 $

$ \frac{x}{15} = \frac{6}{5} $ → $ x = \frac{6 \times 15}{5} = 18 $

✔ Answer: 18

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#### 20) 72 : ___ = 16 : 18

Simplify $ 16:18 $ → divide by 2 → $ 8:9 $

So $ 72:x = 8:9 $

Now, $ 72 \div 8 = 9 $, so $ x = 9 \times 9 = 81 $

✔ Answer: 81

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✔ Final Check:

All answers in the Answer Key match the ones we calculated:

| Problem | Answer |
|--------|--------|
| 1 | 18 |
| 2 | 9 |
| 3 | 18 |
| 4 | 14 |
| 5 | 72 |
| 6 | 24 |
| 7 | 10 |
| 8 | 35 |
| 9 | 4 |
| 10 | 2 |
| 11 | 7 |
| 12 | 9 |
| 13 | 4 |
| 14 | 27 |
| 15 | 32 |
| 16 | 18 |
| 17 | 3 |
| 18 | 15 |
| 19 | 18 |
| 20 | 81 |

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🎯 Summary:

To solve equivalent ratio problems:
1. Simplify the known ratio.
2. Use multiplication or division to scale it to match the unknown.
3. Or use cross-multiplication to solve algebraically.

This worksheet is excellent practice for understanding proportional relationships and scaling ratios.

Let me know if you'd like this turned into a printable explanation sheet or need more practice problems!