Ratio Tables Worksheets - Math Monks - Free Printable

To solve these ratio tables, we need to find the constant relationship (ratio) between `x` and `y` in each table — that is, determine how `y` changes as `x` changes. Usually, this is a multiplicative relationship: `y = k * x` or `x = k * y`, where `k` is a constant.

Let’s go one by one.

---

(1)

```
x | 1 | 4 | 5 | 9
y | 2 | __|10 |__
```

From first pair: `x=1, y=2` → ratio `y/x = 2/1 = 2` → so `y = 2x`

- When `x=4`, `y = 2*4 = 8`
- When `x=9`, `y = 2*9 = 18`

✔ Answer: 8, 18

---

(2)

```
x | 9 |27 |__ |__
y | 1 |__ |4 |8
```

From first pair: `x=9, y=1` → ratio `y/x = 1/9` → so `y = x/9`

- When `x=27`, `y = 27/9 = 3`
- When `y=4`, `x = 4 * 9 = 36`
- When `y=8`, `x = 8 * 9 = 72`

✔ Answer: 3, 36, 72

---

(3)

```
x | 5 |__ |__ |6
y |25 |10 |50 |__
```

From first pair: `x=5, y=25` → ratio `y/x = 25/5 = 5` → `y = 5x`

- When `y=10`, `x = 10/5 = 2`
- When `y=50`, `x = 50/5 = 10`
- When `x=6`, `y = 5*6 = 30`

✔ Answer: 2, 10, 30

---

(4)

```
x |__ |4 |__ |__
y |6 |8 |4 |16
```

Look at `x=4, y=8` → `y/x = 8/4 = 2` → `y = 2x`

- When `y=6`, `x = 6/2 = 3`
- When `y=4`, `x = 4/2 = 2`
- When `y=16`, `x = 16/2 = 8`

✔ Answer: 3, 2, 8

---

(5)

```
x |1 |9 |__ |8
y |5 |__|50 |__
```

From `x=1, y=5` → `y = 5x`

- When `x=9`, `y = 5*9 = 45`
- When `y=50`, `x = 50/5 = 10`
- When `x=8`, `y = 5*8 = 40`

✔ Answer: 45, 10, 40

---

(6)

```
x |4 |__ |__ |5
y |24|18 |60 |__
```

From `x=4, y=24` → `y/x = 24/4 = 6` → `y = 6x`

- When `y=18`, `x = 18/6 = 3`
- When `y=60`, `x = 60/6 = 10`
- When `x=5`, `y = 6*5 = 30`

✔ Answer: 3, 10, 30

---

(7)

```
x |8 |__ |56 |72
y |2 |10 |__ |__
```

From `x=8, y=2` → `y/x = 2/8 = 1/4` → `y = x/4`

- When `y=10`, `x = 10 * 4 = 40`
- When `x=56`, `y = 56/4 = 14`
- When `x=72`, `y = 72/4 = 18`

✔ Answer: 40, 14, 18

---

(8)

```
x |7 |__ |__ |63
y |2 |6 |12 |__
```

From `x=7, y=2` → `y/x = 2/7` → `y = (2/7)x`

Check with next: if `y=6`, then `x = 6 * 7 / 2 = 21`

If `y=12`, `x = 12 * 7 / 2 = 42`

If `x=63`, `y = (2/7)*63 = 18`

✔ Answer: 21, 42, 18

---

(9)

```
x |10 |__ |15 |18
y |__ |80 |__ |72
```

Try ratio: from last pair `x=18, y=72` → `y/x = 72/18 = 4` → `y = 4x`

Check with `x=15`: `y = 4*15 = 60`

When `y=80`, `x = 80/4 = 20`

When `x=10`, `y = 4*10 = 40`

✔ Answer: 40, 20, 60

---

(10)

```
x |6 |20 |__ |10
y |__ |60 |42 |__
```

From `x=20, y=60` → `y/x = 60/20 = 3` → `y = 3x`

- When `x=6`, `y = 3*6 = 18`
- When `y=42`, `x = 42/3 = 14`
- When `x=10`, `y = 3*10 = 30`

✔ Answer: 18, 14, 30

---

(11)

```
x |3 |10 |4 |5
y |12|__ |__|__
```

From `x=3, y=12` → `y/x = 12/3 = 4` → `y = 4x`

- When `x=10`, `y = 4*10 = 40`
- When `x=4`, `y = 4*4 = 16`
- When `x=5`, `y = 4*5 = 20`

✔ Answer: 40, 16, 20

---

(12)

```
x |6 |12 |18 |24
y |4 |__ |__ |__
```

From `x=6, y=4` → `y/x = 4/6 = 2/3` → `y = (2/3)x`

- When `x=12`, `y = (2/3)*12 = 8`
- When `x=18`, `y = (2/3)*18 = 12`
- When `x=24`, `y = (2/3)*24 = 16`

✔ Answer: 8, 12, 16

---

## ✔ Final Answers:

(1) 8, 18
(2) 3, 36, 72
(3) 2, 10, 30
(4) 3, 2, 8
(5) 45, 10, 40
(6) 3, 10, 30
(7) 40, 14, 18
(8) 21, 42, 18
(9) 40, 20, 60
(10) 18, 14, 30
(11) 40, 16, 20
(12) 8, 12, 16

---

## 💡 Key Strategy:
Always find the constant of proportionality (`k`) using a known pair `(x, y)`:

- If `y = k * x`, then `k = y/x`
- If `x = k * y`, then `k = x/y`

Then use it to fill in missing values.

This method works for all proportional relationships — which is what ratio tables are designed for!