Math worksheet for creating equivalent ratios, designed to help students practice finding missing values in proportional relationships.

Let's solve each problem step by step. The goal is to create equivalent ratios by finding the missing number that makes the two ratios equal.

We use the idea that:

> If $ a:b = c:d $, then $ \frac{a}{b} = \frac{c}{d} $, and we can cross-multiply or scale up/down proportionally.

---

(1) $ 8:3 = \_\_ : 27 $

We want to find what number $ x $ makes $ 8:3 = x:27 $.
Since $ 3 \times 9 = 27 $, multiply both parts of the ratio $ 8:3 $ by 9:
$$
8 \times 9 = 72,\quad 3 \times 9 = 27
\Rightarrow 72:27
$$
✔ Answer: 72

---

(2) $ 15 : \_\_ = 24 : 56 $

Simplify $ 24:56 $: divide both by 8 → $ 3:7 $.
So $ 15:x = 3:7 $.
Now, $ 15 \div 3 = 5 $, so multiply $ 3:7 $ by 5 → $ 15:35 $

✔ Answer: 35

---

(3) $ 8:24 = 1:\_\_ $

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

✔ Answer: 3

---

(4) $ 12 : \_\_ = 16 : 24 $

Simplify $ 16:24 $: divide by 8 → $ 2:3 $
So $ 12:x = 2:3 $

Now, $ 12 \div 2 = 6 $, so multiply $ 2:3 $ by 6 → $ 12:18 $

✔ Answer: 18

---

(5) $ 7:56 = \_\_:72 $

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

Now find $ x $ such that $ x:72 = 1:8 $

So $ x = 72 \div 8 = 9 $

✔ Answer: 9

---

(6) $ \_\_:20 = 8:5 $

We have $ x:20 = 8:5 $

Cross-multiply: $ 5x = 8 \times 20 = 160 $ → $ x = 160 \div 5 = 32 $

✔ Answer: 32

---

(7) $ 40:25 = 8:\_\_ $

Simplify $ 40:25 $: divide by 5 → $ 8:5 $

So $ 8:5 $ → answer is 5

✔ Answer: 5

---

(8) $ 5 : \_\_ = 1:7 $

We know $ 5:x = 1:7 $

$ 5 \div 1 = 5 $, so multiply $ 1:7 $ by 5 → $ 5:35 $

✔ Answer: 35

---

(9) $ 12:5 = 72:\_\_ $

$ 12 \times 6 = 72 $, so multiply both sides of $ 12:5 $ by 6 → $ 72:30 $

✔ Answer: 30

---

(10) $ 8 : \_\_ = 1:9 $

$ 8:x = 1:9 $

$ 8 \div 1 = 8 $, so multiply $ 1:9 $ by 8 → $ 8:72 $

✔ Answer: 72

---

(11) $ 20:28 = 5:\_\_ $

Simplify $ 20:28 $: divide by 4 → $ 5:7 $

✔ Answer: 7

---

(12) $ 99 : \_\_ = 11:7 $

We have $ 99:x = 11:7 $

Divide 99 by 11 → $ 99 \div 11 = 9 $, so multiply $ 11:7 $ by 9 → $ 99:63 $

✔ Answer: 63

---

(13) $ 27:72 = 3:\_\_ $

Simplify $ 27:72 $: divide by 9 → $ 3:8 $

✔ Answer: 8

---

(14) $ 9:2 = \_\_:18 $

We want $ x:18 = 9:2 $

$ 18 \div 2 = 9 $, so multiply $ 9:2 $ by 9 → $ 81:18 $

✔ Answer: 81

---

(15) $ 12:7 = \_\_:56 $

$ 56 \div 7 = 8 $, so multiply $ 12:7 $ by 8 → $ 96:56 $

✔ Answer: 96

---

(16) $ 5:35 = 1:\_\_ $

Simplify $ 5:35 $ → divide by 5 → $ 1:7 $

✔ Answer: 7

---

(17) $ 55:25 = \_\_:5 $

Simplify $ 55:25 $: divide by 5 → $ 11:5 $

So $ 11:5 $ → answer is 11

✔ Answer: 11

---

(18) $ 5:10 = 25:\_\_ $

Simplify $ 5:10 $ → $ 1:2 $

Now $ 25:x = 1:2 $

Multiply $ 1:2 $ by 25 → $ 25:50 $

✔ Answer: 50

---

(19) $ 48:28 = 12:\_\_ $

Simplify $ 48:28 $: divide by 4 → $ 12:7 $

✔ Answer: 7

---

(20) $ \_\_:27 = 8:9 $

We have $ x:27 = 8:9 $

$ 27 \div 9 = 3 $, so multiply $ 8:9 $ by 3 → $ 24:27 $

✔ Answer: 24

---

✔ Final Answers:

| Problem | Answer |
|--------|--------|
| (1) | 72 |
| (2) | 35 |
| (3) | 3 |
| (4) | 18 |
| (5) | 9 |
| (6) | 32 |
| (7) | 5 |
| (8) | 35 |
| (9) | 30 |
| (10) | 72 |
| (11) | 7 |
| (12) | 63 |
| (13) | 8 |
| (14) | 81 |
| (15) | 96 |
| (16) | 7 |
| (17) | 11 |
| (18) | 50 |
| (19) | 7 |
| (20) | 24 |

Let me know if you'd like this as a printable sheet or with explanations for each!