Let's solve each proportion using
cross multiplication. Cross multiplication is a method used to solve proportions of the form:
$$
\frac{a}{b} = \frac{c}{d}
$$
You multiply the numerator of one fraction by the denominator of the other:
$$
a \cdot d = b \cdot c
$$
Then solve for the unknown variable.
---
1. $\frac{x}{6} = \frac{15}{18}$
Cross multiply:
$$
x \cdot 18 = 6 \cdot 15 \\
18x = 90 \\
x = \frac{90}{18} = 5
$$
✔ Answer: $x = 5$
---
2. $\frac{x}{3} = \frac{16}{24}$
Cross multiply:
$$
x \cdot 24 = 3 \cdot 16 \\
24x = 48 \\
x = \frac{48}{24} = 2
$$
✔ Answer: $x = 2$
---
3. $\frac{3}{5} = \frac{x}{15}$
Cross multiply:
$$
3 \cdot 15 = 5 \cdot x \\
45 = 5x \\
x = \frac{45}{5} = 9
$$
✔ Answer: $x = 9$
---
4. $\frac{x}{6} = \frac{2}{12}$
Cross multiply:
$$
x \cdot 12 = 6 \cdot 2 \\
12x = 12 \\
x = \frac{12}{12} = 1
$$
✔ Answer: $x = 1$
---
5. $\frac{x}{5} = \frac{18}{20}$
Cross multiply:
$$
x \cdot 20 = 5 \cdot 18 \\
20x = 90 \\
x = \frac{90}{20} = 4.5
$$
✔ Answer: $x = 4.5$ 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: $x = 4$
---
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: $x = \frac{80}{7}$ (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: $x = 1$
---
9. $\frac{9}{4} = \frac{x}{12}$
Cross multiply:
$$
9 \cdot 12 = 4 \cdot x \\
108 = 4x \\
x = \frac{108}{4} = 27
$$
✔ Answer: $x = 27$
---
10. $\frac{1}{3} = \frac{x}{3}$
Cross multiply:
$$
1 \cdot 3 = 3 \cdot x \\
3 = 3x \\
x = \frac{3}{3} = 1
$$
✔ Answer: $x = 1$
---
11. $\frac{x}{2} = \frac{4}{8}$
This is the same as #8:
$$
x \cdot 8 = 2 \cdot 4 \\
8x = 8 \\
x = 1
$$
✔ Answer: $x = 1$
---
12. $\frac{x}{2} = \frac{10}{20}$
Cross multiply:
$$
x \cdot 20 = 2 \cdot 10 \\
20x = 20 \\
x = \frac{20}{20} = 1
$$
✔ Answer: $x = 1$
---
✔ Final Answers:
| Problem | Answer |
|--------|--------|
| 1 | 5 |
| 2 | 2 |
| 3 | 9 |
| 4 | 1 |
| 5 | 4.5 or $\frac{9}{2}$ |
| 6 | 4 |
| 7 | $\frac{80}{7}$ or $11\frac{3}{7}$ |
| 8 | 1 |
| 9 | 27 |
| 10 | 1 |
| 11 | 1 |
| 12 | 1 |
---
📝 Summary:
- Use cross multiplication: $a/b = c/d$ → $a \cdot d = b \cdot c$
- Solve for the unknown.
- Simplify fractions when needed.
Let me know if you'd like these explained step-by-step in a printable format!
Parent Tip: Review the logic above to help your child master the concept of proportion worksheet.
