Ratio Tables Worksheets - Free Printable

Let's solve each of the equivalent ratio tables step by step. The goal is to fill in the missing numbers so that each row maintains an equivalent ratio (i.e., the ratio between the top and bottom numbers remains constant across each column).

---

🔹 Table 1

```
| 21 | | | |
----|----|---|---|---|
6 | 18 |54 |72 |
```

We know:
- First column: 6 → 21 → ratio = 21/6 = 3.5
- So, every top number = bottom × 3.5

Now apply:
- 18 × 3.5 = 63 → second top
- 54 × 3.5 = 189 → third top
- 72 × 3.5 = 252 → fourth top

✔ Completed:
```
| 21 | 63 | 189 | 252 |
----|----|----|-----|-----|
6 | 18 |54 |72 |
```

---

🔹 Table 2

```
| 11 | | 22 | 5.5 |
----|----|---|----|-----|
18 | 54 | | | |
```

Find the ratio from first column:
11 / 18 ≈ ?
But 54 / 18 = 3 → So bottom row multiplies by 3.

So, top row must also multiply by 3:
- 11 × 3 = 33 → second top
- 22 × 3 = 66 → fourth top
- 5.5 × 3 = 16.5 → fifth top

Wait — but we need to check consistency.

Wait — let’s look at known values:

First column: 11 and 18 → ratio = 11/18

Second column: 54 is given in bottom → top = ?
If ratio is constant: top = 54 × (11/18) = 33 ✔

Third column: 22 (top), bottom = ?
bottom = 22 × (18/11) = 36

Fourth column: 5.5 (top), bottom = 5.5 × (18/11) = 9

✔ So completed:
```
| 11 | 33 | 22 | 5.5 |
----|----|----|----|-----|
18 | 54 | 36 | 9 | |
```

Wait — but last column bottom is missing? Let's see: 5.5 / x = 11 / 18 → x = 5.5 × 18 / 11 = 9 ✔

So yes:
```
| 11 | 33 | 22 | 5.5 |
----|----|----|----|-----|
18 | 54 | 36 | 9 | 9 |
```

Wait! Bottom right is blank — but we just found it's 9.

But wait — 5.5 corresponds to bottom 9?

Yes: 5.5 / 9 = 11/18 → correct.

✔ Final:
```
| 11 | 33 | 22 | 5.5 |
----|----|----|----|-----|
18 | 54 | 36 | 9 | 9 |
```

---

🔹 Table 3

```
| | | 12 | 120 |
----|---|---|----|-----|
0.5| 2 | 10 | | |
```

We can find ratio from third column: 12 / 10 = 1.2

So top = bottom × 1.2

Apply:
- First column: 0.5 × 1.2 = 0.6 → top
- Second: 2 × 1.2 = 2.4 → top
- Fourth: 120 / 1.2 = 100 → bottom

Wait — no: if top = bottom × 1.2 → then bottom = top / 1.2

So for fourth column: top = 120 → bottom = 120 / 1.2 = 100

So table becomes:
```
| 0.6 | 2.4 | 12 | 120 |
----|-----|-----|----|-----|
0.5| 2 | 10 | | 100 |
```

Wait — third column bottom is 10 → top is 12 → ratio = 12/10 = 1.2 ✔

So:
- First: top = 0.5 × 1.2 = 0.6
- Second: top = 2 × 1.2 = 2.4
- Fourth: bottom = 120 / 1.2 = 100

✔ Done:
```
| 0.6 | 2.4 | 12 | 120 |
----|-----|-----|----|-----|
0.5| 2 | 10 | | 100 |
```

---

🔹 Table 4

```
| | | | 15 |
----|---|---|---|----|
135 | 50| 70| 75 |
```

Look at last column: top = 15, bottom = 75 → ratio = 15 / 75 = 0.2

So top = bottom × 0.2

Then:
- First: 135 × 0.2 = 27
- Second: 50 × 0.2 = 10
- Third: 70 × 0.2 = 14

✔ Table:
```
| 27 | 10 | 14 | 15 |
----|----|----|----|----|
135 | 50 | 70 | 75 | |
```

---

🔹 Table 5

```
| 0.3 | 9 | | 3 |
----|-----|---|---|---|
1 | | 16| | |
```

First column: 0.3 / 1 = 0.3 → ratio = 0.3

So top = bottom × 0.3

Check second column: top = 9 → bottom = 9 / 0.3 = 30

Third column: bottom = 16 → top = 16 × 0.3 = 4.8

Fourth column: top = 3 → bottom = 3 / 0.3 = 10

✔ So:
```
| 0.3 | 9 | 4.8 | 3 |
----|-----|----|-----|----|
1 | | 16 | | 10 |
```

Missing bottom left? No — bottom left is 1, already there.

So bottom second is 30, bottom third is blank → 16, bottom fourth is 10

Wait — bottom row: 1, ?, 16, ?

We have:
- Second: 30
- Fourth: 10

So:
```
| 0.3 | 9 | 4.8 | 3 |
----|-----|----|-----|----|
1 | | 30 | 16 | 10 |
```

Wait — but third column bottom is 16 → top = 4.8 → ratio = 4.8 / 16 = 0.3 ✔

Yes.

✔ Done.

---

🔹 Table 6

```
| 39 | | 78 | 52 |
----|----|---|----|----|
| 30 | 90| | |
```

First column: 39 / 30 = 1.3 → ratio = 1.3

So top = bottom × 1.3

Second column: bottom = 90 → top = 90 × 1.3 = 117

Third: top = 78 → bottom = 78 / 1.3 = 60

Fourth: top = 52 → bottom = 52 / 1.3 = 40

✔ So:
```
| 39 | 117 | 78 | 52 |
----|----|-----|----|----|
| 30 | 90 | 60 | 40 |
```

---

🔹 Table 7

```
| 20 | | 24 | 15 |
----|----|---|----|----|
16 | 10 | | | |
```

First column: 20 / 16 = 1.25 → ratio = 1.25

So top = bottom × 1.25

Second: bottom = 10 → top = 10 × 1.25 = 12.5

Third: top = 24 → bottom = 24 / 1.25 = 19.2

Fourth: top = 15 → bottom = 15 / 1.25 = 12

✔ Table:
```
| 20 | 12.5 | 24 | 15 |
----|----|------|----|----|
16 | 10 | | 19.2 | 12 |
```

---

🔹 Table 8

```
| | 48 | 3 | |
----|---|----|---|---|
20 | 80 | | 60 |
```

Second column: 48 / 80 = 0.6 → ratio = 0.6

So top = bottom × 0.6

First: bottom = 20 → top = 20 × 0.6 = 12

Third: top = 3 → bottom = 3 / 0.6 = 5

Fourth: bottom = 60 → top = 60 × 0.6 = 36

✔ Table:
```
| 12 | 48 | 3 | 36 |
----|----|----|---|----|
20 | 80 | 5 | 60 |
```

---

🔹 Table 9

```
| | | | 62 |
----|---|---|---|----|
36 | 48 | 54 | 186 |
```

Last column: 62 / 186 = ? → simplify: divide both by 2 → 31 / 93 = 1/3 → so ratio = 1/3

So top = bottom × (1/3)

So:
- First: 36 × 1/3 = 12
- Second: 48 × 1/3 = 16
- Third: 54 × 1/3 = 18

✔ Table:
```
| 12 | 16 | 18 | 62 |
----|----|----|----|----|
36 | 48 | 54 | 186 |
```

---

🔹 Table 10

```
| 15 | | | 0.2 |
----|----|---|---|-----|
45 | 0.9 | 36 | |
```

First column: 15 / 45 = 0.333... = 1/3 → ratio = 1/3

So top = bottom × (1/3)

Second: bottom = 0.9 → top = 0.9 × (1/3) = 0.3

Third: bottom = 36 → top = 36 × (1/3) = 12

Fourth: top = 0.2 → bottom = 0.2 / (1/3) = 0.2 × 3 = 0.6

✔ Table:
```
| 15 | 0.3 | 12 | 0.2 |
----|----|-----|----|-----|
45 | 0.9 | 36 | 0.6 |
```

---

🔹 Table 11

```
| | 40 | 36 | |
----|---|----|----|---|
50 | | 90 | 150 |
```

Second column: 40 / 90 = 4/9 → ratio = 4/9

So top = bottom × (4/9)

First: bottom = 50 → top = 50 × 4/9 = 200/9 ≈ 22.222... → keep as fraction or decimal?

But let's check others.

Third: top = 36 → bottom = 90 → 36 / 90 = 0.4 = 2/5 → not consistent?

Wait — contradiction.

Wait: 40 / 90 = 4/9 ≈ 0.444...

36 / 90 = 0.4 → different!

Wait — so maybe the ratio isn't constant?

Wait — perhaps I misread.

Wait — the same column should be proportional.

But here:

- Column 2: top = 40, bottom = 90 → ratio = 40/90 = 4/9
- Column 3: top = 36, bottom = 90 → ratio = 36/90 = 2/5 → not equal

That can't be — unless the ratio is per row?

No — it's a ratio table — meaning each column has same ratio, and rows are scaled versions.

Wait — actually, each column should maintain the same ratio between top and bottom.

But here:
- Column 2: 40 / 90 = 4/9
- Column 3: 36 / 90 = 36/90 = 2/5 ≠ 4/9

So something wrong?

Wait — perhaps I misread the table.

Let me write clearly:

```
| | 40 | 36 | |
----|---|----|----|---|
50 | | 90 | 150 |
```

So:
- Column 1: top = ?, bottom = 50
- Column 2: top = 40, bottom = 90
- Column 3: top = 36, bottom = 90 → wait, bottom is 90 again?

But two columns have bottom = 90? That's possible.

But ratios:
- Col2: 40 / 90 = 4/9
- Col3: 36 / 90 = 36/90 = 2/5 → not same

But that would mean inconsistent ratio — impossible.

Unless the ratio is between columns, i.e., the top row and bottom row are proportional.

Ah! Wait — this is a ratio table: the top row and bottom row are proportional — so each column has the same ratio: top / bottom = constant.

So all columns must have same ratio.

But here:
- Col2: 40 / 90 = 4/9
- Col3: 36 / 90 = 36/90 = 2/5 → not equal

So contradiction.

Wait — unless I made a mistake.

Wait — is the bottom row: 50, ?, 90, 150

So:
- Col1: top=?, bottom=50
- Col2: top=40, bottom=?
- Col3: top=36, bottom=90
- Col4: top=?, bottom=150

I think I misread earlier.

Looking back:

```
| | 40 | 36 | |
----|---|----|----|---|
50 | | 90 | 150 |
```

So:
- Col1: top=?, bottom=50
- Col2: top=40, bottom=? → wait, bottom is missing!
- Col3: top=36, bottom=90
- Col4: top=?, bottom=150

Ah! So bottom row is: 50, ?, 90, 150

Top row: ?, 40, 36, ?

So we can use col3: top=36, bottom=90 → ratio = 36/90 = 0.4

So ratio = 0.4

Then:
- Col2: top=40 → bottom = 40 / 0.4 = 100
- Col1: bottom=50 → top = 50 × 0.4 = 20
- Col4: bottom=150 → top = 150 × 0.4 = 60

✔ So:
```
| 20 | 40 | 36 | 60 |
----|----|----|----|----|
50 | 100 | 90 | 150 |
```

Now check: 20/50 = 0.4, 40/100 = 0.4, 36/90 = 0.4, 60/150 = 0.4 ✔

Perfect.

---

🔹 Table 12

```
| 24 | | 28 | 20 |
----|----|---|----|----|
| 90 | 63 | | |
```

First column: 24 / 90 = 4/15 → ratio = 4/15

So top = bottom × (4/15)

Second: bottom = 63 → top = 63 × 4/15 = (63×4)/15 = 252/15 = 16.8

Third: top = 28 → bottom = 28 / (4/15) = 28 × 15/4 = 105

Fourth: top = 20 → bottom = 20 × 15/4 = 300/4 = 75

✔ So:
```
| 24 | 16.8 | 28 | 20 |
----|----|------|----|----|
| 90 | 63 | 105 | 75 |
```

---

## ✔ Final Answer Summary:

Here are all completed tables:

---

1.
```
| 21 | 63 | 189 | 252 |
----|----|----|-----|-----|
6 | 18 |54 |72 |
```

2.
```
| 11 | 33 | 22 | 5.5 |
----|----|----|----|-----|
18 | 54 | 36 | 9 | 9 |
```

3.
```
| 0.6 | 2.4 | 12 | 120 |
----|-----|-----|----|-----|
0.5| 2 | 10 | | 100 |
```

4.
```
| 27 | 10 | 14 | 15 |
----|----|----|----|----|
135 | 50 | 70 | 75 | |
```

5.
```
| 0.3 | 9 | 4.8 | 3 |
----|-----|----|-----|----|
1 | | 30 | 16 | 10 |
```

6.
```
| 39 | 117 | 78 | 52 |
----|----|-----|----|----|
| 30 | 90 | 60 | 40 |
```

7.
```
| 20 | 12.5 | 24 | 15 |
----|----|------|----|----|
16 | 10 | | 19.2 | 12 |
```

8.
```
| 12 | 48 | 3 | 36 |
----|----|----|---|----|
20 | 80 | 5 | 60 |
```

9.
```
| 12 | 16 | 18 | 62 |
----|----|----|----|----|
36 | 48 | 54 | 186 |
```

10.
```
| 15 | 0.3 | 12 | 0.2 |
----|----|-----|----|-----|
45 | 0.9 | 36 | 0.6 |
```

11.
```
| 20 | 40 | 36 | 60 |
----|----|----|----|----|
50 | 100 | 90 | 150 |
```

12.
```
| 24 | 16.8 | 28 | 20 |
----|----|------|----|----|
| 90 | 63 | 105 | 75 |
```

---

✔ How to Solve:

For each table:
1. Find the ratio between known top and bottom values in any column.
2. Use that ratio to compute missing values.
3. Ensure all columns have the same ratio (top/bottom).
4. If multiple entries, verify consistency.

This ensures equivalent ratios across the table.

Let me know if you'd like this formatted as a printable answer sheet!