Practice sheet featuring twelve problems where students must use cross multiplication to find the missing numerator or denominator.

To solve the given proportions using cross multiplication, we will follow these steps:

Cross Multiplication Method:

For a proportion of the form \( \frac{a}{b} = \frac{c}{d} \), cross multiplication gives:
\[ a \cdot d = b \cdot c \]

We will use this method to solve each problem.

---

Problem 1: \( \frac{x}{6} = \frac{15}{18} \)

1. Cross multiply:
\[
x \cdot 18 = 6 \cdot 15
\]
2. Simplify:
\[
18x = 90
\]
3. Solve for \( x \):
\[
x = \frac{90}{18} = 5
\]

Answer: \( x = 5 \)

---

Problem 2: \( \frac{x}{3} = \frac{16}{24} \)

1. Cross multiply:
\[
x \cdot 24 = 3 \cdot 16
\]
2. Simplify:
\[
24x = 48
\]
3. Solve for \( x \):
\[
x = \frac{48}{24} = 2
\]

Answer: \( x = 2 \)

---

Problem 3: \( \frac{3}{5} = \frac{x}{15} \)

1. Cross multiply:
\[
3 \cdot 15 = 5 \cdot x
\]
2. Simplify:
\[
45 = 5x
\]
3. Solve for \( x \):
\[
x = \frac{45}{5} = 9
\]

Answer: \( x = 9 \)

---

Problem 4: \( \frac{x}{6} = \frac{2}{12} \)

1. Cross multiply:
\[
x \cdot 12 = 6 \cdot 2
\]
2. Simplify:
\[
12x = 12
\]
3. Solve for \( x \):
\[
x = \frac{12}{12} = 1
\]

Answer: \( x = 1 \)

---

Problem 5: \( \frac{x}{5} = \frac{16}{20} \)

1. Cross multiply:
\[
x \cdot 20 = 5 \cdot 16
\]
2. Simplify:
\[
20x = 80
\]
3. Solve for \( x \):
\[
x = \frac{80}{20} = 4
\]

Answer: \( x = 4 \)

---

Problem 6: \( \frac{1}{2} = \frac{x}{8} \)

1. Cross multiply:
\[
1 \cdot 8 = 2 \cdot x
\]
2. Simplify:
\[
8 = 2x
\]
3. Solve for \( x \):
\[
x = \frac{8}{2} = 4
\]

Answer: \( x = 4 \)

---

Problem 7: \( \frac{x}{8} = \frac{10}{16} \)

1. Cross multiply:
\[
x \cdot 16 = 8 \cdot 10
\]
2. Simplify:
\[
16x = 80
\]
3. Solve for \( x \):
\[
x = \frac{80}{16} = 5
\]

Answer: \( x = 5 \)

---

Problem 8: \( \frac{x}{2} = \frac{4}{8} \)

1. Cross multiply:
\[
x \cdot 8 = 2 \cdot 4
\]
2. Simplify:
\[
8x = 8
\]
3. Solve for \( x \):
\[
x = \frac{8}{8} = 1
\]

Answer: \( x = 1 \)

---

Problem 9: \( \frac{x}{4} = \frac{9}{12} \)

1. Cross multiply:
\[
x \cdot 12 = 4 \cdot 9
\]
2. Simplify:
\[
12x = 36
\]
3. Solve for \( x \):
\[
x = \frac{36}{12} = 3
\]

Answer: \( x = 3 \)

---

Problem 10: \( \frac{1}{3} = \frac{x}{3} \)

1. Cross multiply:
\[
1 \cdot 3 = 3 \cdot x
\]
2. Simplify:
\[
3 = 3x
\]
3. Solve for \( x \):
\[
x = \frac{3}{3} = 1
\]

Answer: \( x = 1 \)

---

Problem 11: \( \frac{x}{2} = \frac{4}{8} \)

1. Cross multiply:
\[
x \cdot 8 = 2 \cdot 4
\]
2. Simplify:
\[
8x = 8
\]
3. Solve for \( x \):
\[
x = \frac{8}{8} = 1
\]

Answer: \( x = 1 \)

---

Problem 12: \( \frac{x}{2} = \frac{10}{20} \)

1. Cross multiply:
\[
x \cdot 20 = 2 \cdot 10
\]
2. Simplify:
\[
20x = 20
\]
3. Solve for \( x \):
\[
x = \frac{20}{20} = 1
\]

Answer: \( x = 1 \)

---

Final Answers:

\[
\boxed{
\begin{aligned}
1. & \ x = 5 \\
2. & \ x = 2 \\
3. & \ x = 9 \\
4. & \ x = 1 \\
5. & \ x = 4 \\
6. & \ x = 4 \\
7. & \ x = 5 \\
8. & \ x = 1 \\
9. & \ x = 3 \\
10. & \ x = 1 \\
11. & \ x = 1 \\
12. & \ x = 1 \\
\end{aligned}
}
\]