Equivalent Ratio Worksheets - Math Monks - Free Printable

Let's solve each of these equivalent ratio tables step by step. The goal is to fill in the missing numbers so that the ratios between the top and bottom rows remain equivalent (i.e., the same).

---

1.

```
Top: 1 2 3 5
Bot: 6 ? ? ?
```

- Ratio from first column: $ \frac{6}{1} = 6 $
- So multiply each top number by 6:
- $ 2 \times 6 = 12 $
- $ 3 \times 6 = 18 $
- $ 5 \times 6 = 30 $

✔ Answer:
```
Top: 1 2 3 5
Bot: 6 12 18 30
```

---

2.

```
Top: 7 ? ? ?
Bot: 5 10 25 30
```

- First ratio: $ \frac{5}{7} $ → not a whole number, but we can use cross-multiplication or find multiplier.
- Let’s find the ratio between top and bottom: $ \frac{7}{5} $, so bottom values are multiplied by $ \frac{5}{7} $? Wait — better to reverse.

We know:
- $ \frac{7}{x} = \frac{5}{10} = \frac{1}{2} $ → so $ x = 14 $
- Check: $ \frac{7}{14} = \frac{1}{2} $, and $ \frac{5}{10} = \frac{1}{2} $ ✔

Now use this ratio: top / bottom = 1/2 → so top = bottom × 0.5

Wait! Actually, let's check:

From bottom row: 5 → 10 → 25 → 30

But top starts with 7, and bottom is 5.

So ratio: $ \frac{7}{5} = 1.4 $ → top = bottom × 1.4?

Try:
- $ 10 \times 1.4 = 14 $
- $ 25 \times 1.4 = 35 $
- $ 30 \times 1.4 = 42 $

Check: $ \frac{7}{5} = 1.4 $, $ \frac{14}{10} = 1.4 $, $ \frac{35}{25} = 1.4 $, $ \frac{42}{30} = 1.4 $ ✔

So top row: 7, 14, 35, 42

✔ Answer:
```
Top: 7 14 35 42
Bot: 5 10 25 30
```

---

3.

```
Top: ? 4 6 8
Bot: 8 16 ? ?
```

- From second column: $ \frac{4}{16} = \frac{1}{4} $ → so top = bottom × $ \frac{1}{4} $
- Or: bottom = top × 4

So:
- First column: top = $ \frac{8}{4} = 2 $
- Third: bottom = $ 6 \times 4 = 24 $
- Fourth: bottom = $ 8 \times 4 = 32 $

✔ Answer:
```
Top: 2 4 6 8
Bot: 8 16 24 32
```

---

4.

```
Top: 12 3 9 10
Bot: ? ? 18 ?
```

- Third column: $ \frac{9}{18} = \frac{1}{2} $ → so top = bottom × 0.5 → bottom = top × 2
- So all bottom values should be twice the top.

Check:
- Top 12 → bottom = 24
- Top 3 → bottom = 6
- Top 9 → bottom = 18 ✔
- Top 10 → bottom = 20

✔ Answer:
```
Top: 12 3 9 10
Bot: 24 6 18 20
```

---

5.

```
Top: ? ? 10 200
Bot: 12 15 30 ?
```

- Third column: $ \frac{10}{30} = \frac{1}{3} $ → so top = bottom × $ \frac{1}{3} $ → bottom = top × 3
- Use this ratio.

So:
- First: top = $ \frac{12}{3} = 4 $
- Second: top = $ \frac{15}{3} = 5 $
- Fourth: bottom = $ 200 \times 3 = 600 $

✔ Answer:
```
Top: 4 5 10 200
Bot: 12 15 30 600
```

---

6.

```
Top: ? 5 10 ?
Bot: 5 25 ? 250
```

- Second column: $ \frac{5}{25} = \frac{1}{5} $ → so top = bottom × $ \frac{1}{5} $ → bottom = top × 5

So:
- First: top = $ \frac{5}{5} = 1 $
- Third: bottom = $ 10 \times 5 = 50 $
- Fourth: top = $ \frac{250}{5} = 50 $

✔ Answer:
```
Top: 1 5 10 50
Bot: 5 25 50 250
```

---

7.

```
Top: 1 ? 3 4
Bot: ? 34 51 ?
```

- Third column: $ \frac{3}{51} = \frac{1}{17} $ → so top = bottom × $ \frac{1}{17} $ → bottom = top × 17

So:
- First: bottom = $ 1 \times 17 = 17 $
- Second: top = $ \frac{34}{17} = 2 $
- Fourth: bottom = $ 4 \times 17 = 68 $

✔ Answer:
```
Top: 1 2 3 4
Bot: 17 34 51 68
```

---

8.

```
Top: ? 4 8 16
Bot: 10 20 ? ?
```

- Second column: $ \frac{4}{20} = \frac{1}{5} $ → bottom = top × 5

So:
- First: top = $ \frac{10}{5} = 2 $
- Third: bottom = $ 8 \times 5 = 40 $
- Fourth: bottom = $ 16 \times 5 = 80 $

✔ Answer:
```
Top: 2 4 8 16
Bot: 10 20 40 80
```

---

9.

```
Top: 2 4 6 8
Bot: ? ? 36 ?
```

- Third column: $ \frac{6}{36} = \frac{1}{6} $ → so bottom = top × 6

So:
- First: bottom = $ 2 \times 6 = 12 $
- Second: bottom = $ 4 \times 6 = 24 $
- Fourth: bottom = $ 8 \times 6 = 48 $

✔ Answer:
```
Top: 2 4 6 8
Bot: 12 24 36 48
```

---

10.

```
Top: 5 ? ? 6
Bot: 25 10 50 ?
```

- First column: $ \frac{5}{25} = \frac{1}{5} $ → so bottom = top × 5

So:
- Second: top = $ \frac{10}{5} = 2 $
- Third: top = $ \frac{50}{5} = 10 $
- Fourth: bottom = $ 6 \times 5 = 30 $

✔ Answer:
```
Top: 5 2 10 6
Bot: 25 10 50 30
```

---

11.

```
Top: 3 ? 4 5
Bot: 15 50 ? ?
```

- First column: $ \frac{3}{15} = \frac{1}{5} $ → so bottom = top × 5

So:
- Second: top = $ \frac{50}{5} = 10 $
- Third: bottom = $ 4 \times 5 = 20 $
- Fourth: bottom = $ 5 \times 5 = 25 $

✔ Answer:
```
Top: 3 10 4 5
Bot: 15 50 20 25
```

---

12.

```
Top: ? 6 15 9
Bot: 4 2 ? ?
```

- Second column: $ \frac{6}{2} = 3 $ → so top = bottom × 3 → bottom = top ÷ 3

So:
- First: top = $ 4 \times 3 = 12 $
- Third: bottom = $ 15 \div 3 = 5 $
- Fourth: bottom = $ 9 \div 3 = 3 $

✔ Answer:
```
Top: 12 6 15 9
Bot: 4 2 5 3
```

---

## ✔ Final Answers:

1.
```
Top: 1 2 3 5
Bot: 6 12 18 30
```

2.
```
Top: 7 14 35 42
Bot: 5 10 25 30
```

3.
```
Top: 2 4 6 8
Bot: 8 16 24 32
```

4.
```
Top: 12 3 9 10
Bot: 24 6 18 20
```

5.
```
Top: 4 5 10 200
Bot: 12 15 30 600
```

6.
```
Top: 1 5 10 50
Bot: 5 25 50 250
```

7.
```
Top: 1 2 3 4
Bot: 17 34 51 68
```

8.
```
Top: 2 4 8 16
Bot: 10 20 40 80
```

9.
```
Top: 2 4 6 8
Bot: 12 24 36 48
```

10.
```
Top: 5 2 10 6
Bot: 25 10 50 30
```

11.
```
Top: 3 10 4 5
Bot: 15 50 20 25
```

12.
```
Top: 12 6 15 9
Bot: 4 2 5 3
```

---

🔍 How to Solve These:

- Look at any complete pair (top and bottom) to determine the ratio.
- Use that ratio to find missing values.
- You can express it as:
- If $ \frac{\text{top}}{\text{bottom}} = r $, then $ \text{top} = r \times \text{bottom} $
- Or $ \text{bottom} = \frac{\text{top}}{r} $
- Keep the ratio constant across all columns.

Let me know if you'd like a printable version or explanation for a specific one!