Ratio Tables worksheet for practicing proportional relationships and completing missing values in tables.

Let's solve each of these ratio tables step by step. In a ratio table, the relationship between $ x $ and $ y $ is proportional, meaning:

$$
\frac{x}{y} = \text{constant} \quad \text{or} \quad y = kx \quad \text{(where } k \text{ is the constant of proportionality)}
$$

We'll find the constant ratio $ k = \frac{y}{x} $ (or $ \frac{x}{y} $) from known values and use it to fill in the missing entries.

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(1)

$$
\begin{array}{c|cccc}
x & 1 & 4 & 5 & 9 \\
\hline
y & 2 & ? & 10 & ? \\
\end{array}
$$

From $ x=1, y=2 $:
Ratio $ k = \frac{y}{x} = \frac{2}{1} = 2 $

So $ y = 2x $

- When $ x = 4 $: $ y = 2 \times 4 = 8 $
- When $ x = 5 $: $ y = 2 \times 5 = 10 $ ✔
- When $ x = 9 $: $ y = 2 \times 9 = 18 $

✔ Answer: $ y = 8, 10, 18 $

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(2)

$$
\begin{array}{c|cccc}
x & 9 & 27 & ? & ? \\
\hline
y & 1 & ? & 4 & 8 \\
\end{array}
$$

From $ x=9, y=1 $: $ k = \frac{y}{x} = \frac{1}{9} $

So $ y = \frac{1}{9}x $ → $ x = 9y $

- $ x = 27 $: $ y = \frac{1}{9} \times 27 = 3 $
- $ y = 4 $: $ x = 9 \times 4 = 36 $
- $ y = 8 $: $ x = 9 \times 8 = 72 $

✔ Answer: $ y = 3, 4, 8 $; $ x = 36, 72 $

Wait — let’s recheck:

Given:
- $ x=9, y=1 $ → $ k = \frac{y}{x} = \frac{1}{9} $
- So $ y = \frac{1}{9}x $

Then:
- $ x=27 $: $ y = \frac{1}{9} \times 27 = 3 $
- $ y=4 $: $ x = 9 \times 4 = 36 $
- $ y=8 $: $ x = 9 \times 8 = 72 $

So blanks are:
- $ x=27 $ → $ y = 3 $
- $ y=4 $ → $ x = 36 $
- $ y=8 $ → $ x = 72 $

✔ Fill in: $ y = 3 $, then $ x = 36 $, $ x = 72 $

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(3)

$$
\begin{array}{c|cccc}
x & 5 & ? & ? & 6 \\
\hline
y & 25 & 10 & 50 & ? \\
\end{array}
$$

From $ x=5, y=25 $: $ k = \frac{25}{5} = 5 $

So $ y = 5x $

- $ y = 10 $: $ x = \frac{10}{5} = 2 $
- $ y = 50 $: $ x = \frac{50}{5} = 10 $
- $ x = 6 $: $ y = 5 \times 6 = 30 $

✔ Answers: $ x = 2, 10 $; $ y = 30 $

---

(4)

$$
\begin{array}{c|cccc}
x & ? & 4 & ? & ? \\
\hline
y & 6 & 8 & 4 & 16 \\
\end{array}
$$

Use $ x=4, y=8 $: $ k = \frac{8}{4} = 2 $ → $ y = 2x $

So:
- $ y = 6 $: $ x = \frac{6}{2} = 3 $
- $ y = 4 $: $ x = \frac{4}{2} = 2 $
- $ y = 16 $: $ x = \frac{16}{2} = 8 $

✔ Answers: $ x = 3, 2, 8 $

---

(5)

$$
\begin{array}{c|cccc}
x & 1 & 9 & ? & 8 \\
\hline
y & 5 & ? & 50 & ? \\
\end{array}
$$

$ x=1, y=5 $ → $ k = \frac{5}{1} = 5 $ → $ y = 5x $

- $ x=9 $: $ y = 5 \times 9 = 45 $
- $ y=50 $: $ x = \frac{50}{5} = 10 $
- $ x=8 $: $ y = 5 \times 8 = 40 $

✔ Answers: $ y = 45, 50, 40 $; $ x = 10 $

---

(6)

$$
\begin{array}{c|cccc}
x & 4 & ? & ? & 5 \\
\hline
y & 24 & 18 & 60 & ? \\
\end{array}
$$

$ x=4, y=24 $ → $ k = \frac{24}{4} = 6 $ → $ y = 6x $

- $ y = 18 $: $ x = \frac{18}{6} = 3 $
- $ y = 60 $: $ x = \frac{60}{6} = 10 $
- $ x = 5 $: $ y = 6 \times 5 = 30 $

✔ Answers: $ x = 3, 10 $; $ y = 30 $

---

(7)

$$
\begin{array}{c|cccc}
x & 8 & ? & 56 & 72 \\
\hline
y & 2 & 10 & ? & ? \\
\end{array}
$$

$ x=8, y=2 $ → $ k = \frac{2}{8} = \frac{1}{4} $ → $ y = \frac{1}{4}x $

- $ y = 10 $: $ x = 10 \times 4 = 40 $
- $ x = 56 $: $ y = \frac{1}{4} \times 56 = 14 $
- $ x = 72 $: $ y = \frac{1}{4} \times 72 = 18 $

✔ Answers: $ x = 40 $, $ y = 14, 18 $

---

(8)

$$
\begin{array}{c|cccc}
x & 7 & ? & ? & 63 \\
\hline
y & 2 & 6 & 12 & ? \\
\end{array}
$$

$ x=7, y=2 $ → $ k = \frac{2}{7} $ → $ y = \frac{2}{7}x $

- $ y = 6 $: $ x = \frac{6 \times 7}{2} = 21 $
- $ y = 12 $: $ x = \frac{12 \times 7}{2} = 42 $
- $ x = 63 $: $ y = \frac{2}{7} \times 63 = 18 $

✔ Answers: $ x = 21, 42 $; $ y = 18 $

---

(9)

$$
\begin{array}{c|cccc}
x & 10 & ? & 15 & 18 \\
\hline
y & ? & 80 & ? & 72 \\
\end{array}
$$

Use $ x=18, y=72 $: $ k = \frac{72}{18} = 4 $ → $ y = 4x $

Check $ x=10 $: $ y = 4 \times 10 = 40 $

Check $ y=80 $: $ x = \frac{80}{4} = 20 $

Check $ x=15 $: $ y = 4 \times 15 = 60 $

✔ Answers: $ y = 40, 80, 60, 72 $; $ x = 20 $

---

(10)

$$
\begin{array}{c|cccc}
x & 6 & 20 & ? & 10 \\
\hline
y & ? & 60 & 42 & ? \\
\end{array}
$$

Use $ x=20, y=60 $: $ k = \frac{60}{20} = 3 $ → $ y = 3x $

- $ x=6 $: $ y = 3 \times 6 = 18 $
- $ y=42 $: $ x = \frac{42}{3} = 14 $
- $ x=10 $: $ y = 3 \times 10 = 30 $

✔ Answers: $ y = 18, 60, 42, 30 $; $ x = 14 $

---

(11)

$$
\begin{array}{c|cccc}
x & 3 & 10 & 4 & 5 \\
\hline
y & 12 & ? & ? & ? \\
\end{array}
$$

$ x=3, y=12 $ → $ k = \frac{12}{3} = 4 $ → $ y = 4x $

- $ x=10 $: $ y = 4 \times 10 = 40 $
- $ x=4 $: $ y = 4 \times 4 = 16 $
- $ x=5 $: $ y = 4 \times 5 = 20 $

✔ Answers: $ y = 40, 16, 20 $

---

(12)

$$
\begin{array}{c|cccc}
x & 6 & 12 & 18 & 24 \\
\hline
y & 4 & ? & ? & ? \\
\end{array}
$$

$ x=6, y=4 $ → $ k = \frac{4}{6} = \frac{2}{3} $ → $ y = \frac{2}{3}x $

- $ x=12 $: $ y = \frac{2}{3} \times 12 = 8 $
- $ x=18 $: $ y = \frac{2}{3} \times 18 = 12 $
- $ x=24 $: $ y = \frac{2}{3} \times 24 = 16 $

✔ Answers: $ y = 8, 12, 16 $

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✔ Final Answers:

(1)
x: 1, 4, 5, 9
y: 2, 8, 10, 18

(2)
x: 9, 27, 36, 72
y: 1, 3, 4, 8

(3)
x: 5, 2, 10, 6
y: 25, 10, 50, 30

(4)
x: 3, 4, 2, 8
y: 6, 8, 4, 16

(5)
x: 1, 9, 10, 8
y: 5, 45, 50, 40

(6)
x: 4, 3, 10, 5
y: 24, 18, 60, 30

(7)
x: 8, 40, 56, 72
y: 2, 10, 14, 18

(8)
x: 7, 21, 42, 63
y: 2, 6, 12, 18

(9)
x: 10, 20, 15, 18
y: 40, 80, 60, 72

(10)
x: 6, 20, 14, 10
y: 18, 60, 42, 30

(11)
x: 3, 10, 4, 5
y: 12, 40, 16, 20

(12)
x: 6, 12, 18, 24
y: 4, 8, 12, 16

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