7th Grade Math Worksheets - Free Printable

It looks like you've uploaded a worksheet titled "Equivalent Ratios" with two main sections:

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A. Write any two equivalent ratios for each ratio

This section asks you to find two ratios that are equivalent to the given ones.

To find an equivalent ratio, you can multiply or divide both terms of the ratio by the same number.

Let’s go through each one:

#### 1) 1:2
- Multiply by 2: $ 1×2 : 2×2 = 2:4 $
- Multiply by 3: $ 1×3 : 2×3 = 3:6 $
✔ Equivalent ratios: 2:4, 3:6

#### 2) 4:9
- Multiply by 2: $ 4×2 : 9×2 = 8:18 $
- Multiply by 3: $ 4×3 : 9×3 = 12:27 $
✔ Equivalent ratios: 8:18, 12:27

#### 3) 5:8
- Multiply by 2: $ 5×2 : 8×2 = 10:16 $
- Multiply by 3: $ 5×3 : 8×3 = 15:24 $
✔ Equivalent ratios: 10:16, 15:24

#### 4) 7:10
- Multiply by 2: $ 7×2 : 10×2 = 14:20 $
- Multiply by 3: $ 7×3 : 10×3 = 21:30 $
✔ Equivalent ratios: 14:20, 21:30

#### 5) 4:11
- Multiply by 2: $ 4×2 : 11×2 = 8:22 $
- Multiply by 3: $ 4×3 : 11×3 = 12:33 $
✔ Equivalent ratios: 8:22, 12:33

#### 6) 13:1
- Multiply by 2: $ 13×2 : 1×2 = 26:2 $
- Multiply by 3: $ 13×3 : 1×3 = 39:3 $
✔ Equivalent ratios: 26:2, 39:3

#### 7) 9:20
- Multiply by 2: $ 9×2 : 20×2 = 18:40 $
- Multiply by 3: $ 9×3 : 20×3 = 27:60 $
✔ Equivalent ratios: 18:40, 27:60

#### 8) 15:5
First simplify: $ 15:5 = 3:1 $
Now use that:
- Multiply by 2: $ 3×2 : 1×2 = 6:2 $
- Multiply by 3: $ 3×3 : 1×3 = 9:3 $
✔ Equivalent ratios: 6:2, 9:3

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B. Complete the equivalent ratio tables

These are tables where one number is missing, and we need to find it using the concept of equivalent ratios.

---

#### 1)
```
7 21
8 ?
21 63
```

We see that:
- $ 7 → 21 $: multiplied by 3
- So $ 8 × 3 = 24 $

✔ Answer: 24

---

#### 2)
```
5 25 35
9 ? 63
```

Look at first row: $ 5 → 25 $: ×5
$ 5 → 35 $: ×7

Check second row:
- $ 9 × 5 = 45 $
- $ 9 × 7 = 63 $ → matches!

So the missing value is $ 9 × 5 = 45 $

✔ Answer: 45

---

#### 3)
```
? 10 20
15 30 60
```

Second row: $ 15 → 30 $: ×2, $ 15 → 60 $: ×4
So the multiplier from first column to second is ×2, third is ×4

So in first row:
- First number ×2 = 10 → so first number = $ 10 ÷ 2 = 5 $
- Check: $ 5 × 4 = 20 $ → correct

✔ Answer: 5

---

#### 4)
```
11 22 ? 16
```

Wait — this seems misaligned. Let's look carefully.

It says:
```
11 22 ? 16
8 16
```

But the layout is confusing. Let's interpret:

It appears as a table with two rows:

```
11 22 ? 16
8 16
```

Possibly meant to be:

| 11 | 22 | ? | 16 |
|----|----|---|----|
| | 8 | 16| |

But that doesn't make sense. Wait — maybe it's:

```
Row 1: 11 22 ? 16
Row 2: 8 16
```

That still doesn’t align.

Alternatively, perhaps it's:

```
11 22 ? 16
8 16
```

Wait — likely a typo or formatting issue.

Looking at structure: probably intended as:

| 11 | 22 | ? | 16 |
|----|----|---|----|
| | 8 | 16| |

But that doesn't help.

Wait — another possibility: the table is:

```
11 22 ? 16
8 16
```

But only three columns?

Let me re-read:

> 4) 11 22 ? 16
> 8 16

Ah! Likely it's a ratio table with two rows and four columns:

```
11 22 ? 16
8 16
```

No — wait, that can't be. Maybe:

Actually, the format might be:

| | 11 | 22 | ? | 16 |
|---|----|----|---|----|
| | | 8 | 16|

That doesn't work.

Wait — let's assume the table is:

```
Column 1: 11
Column 2: 22, 8
Column 3: ?, 16
Column 4: 16
```

No — better idea: Perhaps the first row is the top, and second row is below, but aligned:

Maybe:

```
11 22 ? 16
8 16
```

But that implies only 3 entries in the second row.

Wait — perhaps it's:

```
11 22 ? 16
8 16
```

Meaning:

- Column 1: 11 (top), nothing below?
- Column 2: 22 (top), 8 (bottom)
- Column 3: ? (top), 16 (bottom)
- Column 4: 16 (top), nothing?

No — not making sense.

Alternative interpretation: It's a two-row table with three columns, but formatted poorly.

Let’s try:

> 4) 11 22 ?
> 8 16

So:

| 11 | 22 | ? |
|----|----|---|
| | 8 | 16|

That suggests:

- Top row: 11, 22, ?
- Bottom row: ?, 8, 16

But first entry missing.

Wait — maybe it's:

```
11 22 ?
8 16
```

And the bottom row has two values: 8 and 16

But then what about the first column?

Possibility: The first column is 11 and something, but only 11 shown.

Wait — perhaps it's:

| 11 | 22 | ? |
|----|----|---|
| | 8 | 16|

But no value under 11.

Another thought: Maybe it's supposed to be:

| 11 | 22 | ? | 16 |
|----|----|---|----|
| | 8 | 16| |

But that would mean 22 corresponds to 8, and ? corresponds to 16, and 16 corresponds to nothing.

Wait — if 22 → 8, then ratio is 22:8 = 11:4

Then ? → 16: so if ratio is 11:4, then:

Let x be the missing number.

We have: $ \frac{x}{16} = \frac{11}{4} $ → $ x = \frac{11}{4} × 16 = 44 $

So missing number is 44

Also, check: 11 → ? — but no value given.

But we have 11 at start, and 22 → 8, so 22/8 = 2.75, and 11 × 2.75 = 29.75? No.

Wait — better: if 22 corresponds to 8, then ratio is 22:8 = 11:4

Then ? corresponds to 16 → so ? / 16 = 11 / 4 → ? = (11 × 16)/4 = 44

So missing number is 44

And 11 → ? — but not needed.

But what about 16 at the end?

Wait — maybe the table is:

```
11 22 ? 16
8 16
```

Perhaps it's a typo, and it should be:

```
11 22 ? 16
8 16
```

With only three columns:

| 11 | 22 | ? |
|----|----|---|
| | 8 | 16|

Then we can say: 22 → 8, and ? → 16

So ratio between top and bottom: 22:8 = 11:4

So ? : 16 = 11:4 → ? = (11 × 16)/4 = 44

✔ So missing number is 44

And 11 is just extra info? Or perhaps the first column is 11 and blank — maybe not used.

Alternatively, maybe the table is:

| 11 | 22 | ? | 16 |
|----|----|---|----|
| | 8 | 16| |

But again, inconsistent.

Given the ambiguity, most logical interpretation:

- We have a ratio: 22 → 8
- Then ? → 16
- So scale factor from 8 to 16 is ×2
- So 22 × 2 = 44

So missing value is 44

✔ Answer: 44

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✔ Final Answers:

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#### Section A: Equivalent Ratios

1) 1:2 → 2:4, 3:6
2) 4:9 → 8:18, 12:27
3) 5:8 → 10:16, 15:24
4) 7:10 → 14:20, 21:30
5) 4:11 → 8:22, 12:33
6) 13:1 → 26:2, 39:3
7) 9:20 → 18:40, 27:60
8) 15:5 → 6:2, 9:3

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#### Section B: Complete the Tables

1) $ 8 \times 3 = 24 $ → 24
2) $ 9 \times 5 = 45 $ → 45
3) $ 10 ÷ 2 = 5 $ → 5
4) $ ? = 44 $ → 44

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