Grade 6 Math Worksheet: Solving proportions | Worsheets library - Free Printable

Let's solve each of these proportion problems using cross multiplication. The general rule for solving proportions is:

If
$$
\frac{a}{b} = \frac{c}{d}
$$
then
$$
a \cdot d = b \cdot c
$$

We'll apply this to each problem.

---

1.

$$
\frac{x}{6} = \frac{15}{18}
$$

Cross multiply:
$$
x \cdot 18 = 6 \cdot 15 \\
18x = 90 \\
x = \frac{90}{18} = 5
$$

✔ Answer: 5

---

2.

$$
\frac{x}{3} = \frac{16}{24}
$$

Cross multiply:
$$
x \cdot 24 = 3 \cdot 16 \\
24x = 48 \\
x = \frac{48}{24} = 2
$$

✔ Answer: 2

---

3.

$$
\frac{3}{5} = \frac{x}{15}
$$

Cross multiply:
$$
3 \cdot 15 = 5 \cdot x \\
45 = 5x \\
x = \frac{45}{5} = 9
$$

✔ Answer: 9

---

4.

$$
\frac{x}{6} = \frac{2}{12}
$$

Cross multiply:
$$
x \cdot 12 = 6 \cdot 2 \\
12x = 12 \\
x = \frac{12}{12} = 1
$$

✔ Answer: 1

---

5.

$$
\frac{x}{5} = \frac{18}{20}
$$

Cross multiply:
$$
x \cdot 20 = 5 \cdot 18 \\
20x = 90 \\
x = \frac{90}{20} = 4.5
$$

✔ Answer: 4.5 (or $ \frac{9}{2} $)

---

6.

$$
\frac{1}{2} = \frac{x}{8}
$$

Cross multiply:
$$
1 \cdot 8 = 2 \cdot x \\
8 = 2x \\
x = \frac{8}{2} = 4
$$

✔ Answer: 4

---

7.

$$
\frac{7}{8} = \frac{10}{x}
$$

Cross multiply:
$$
7 \cdot x = 8 \cdot 10 \\
7x = 80 \\
x = \frac{80}{7} \approx 11.43
$$

✔ Answer: $ \frac{80}{7} $ or $ 11\frac{3}{7} $

---

8.

$$
\frac{x}{2} = \frac{4}{8}
$$

Cross multiply:
$$
x \cdot 8 = 2 \cdot 4 \\
8x = 8 \\
x = \frac{8}{8} = 1
$$

✔ Answer: 1

---

9.

$$
\frac{9}{4} = \frac{x}{12}
$$

Cross multiply:
$$
9 \cdot 12 = 4 \cdot x \\
108 = 4x \\
x = \frac{108}{4} = 27
$$

✔ Answer: 27

---

10.

$$
\frac{1}{3} = \frac{x}{3}
$$

Cross multiply:
$$
1 \cdot 3 = 3 \cdot x \\
3 = 3x \\
x = \frac{3}{3} = 1
$$

✔ Answer: 1

---

11.

$$
\frac{x}{2} = \frac{4}{8}
$$

This is the same as #8.
Cross multiply:
$$
x \cdot 8 = 2 \cdot 4 \\
8x = 8 \\
x = 1
$$

✔ Answer: 1

---

12.

$$
\frac{x}{2} = \frac{10}{20}
$$

Cross multiply:
$$
x \cdot 20 = 2 \cdot 10 \\
20x = 20 \\
x = \frac{20}{20} = 1
$$

✔ Answer: 1

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✔ Final Answers:

1. 5
2. 2
3. 9
4. 1
5. 4.5
6. 4
7. $ \frac{80}{7} $ or $ 11\frac{3}{7} $
8. 1
9. 27
10. 1
11. 1
12. 1

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