Let's solve each proportion using
cross multiplication. Cross multiplication is a method used to solve proportions of the form:
$$
\frac{a}{b} = \frac{c}{d}
$$
By cross multiplying, we get:
$$
a \cdot d = b \cdot c
$$
We’ll apply this to each problem and solve for the missing number.
---
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. $\frac{x}{5} = \frac{16}{20}$
Cross multiply:
$$
x \cdot 20 = 5 \cdot 16 \\
20x = 80 \\
x = \frac{80}{20} = 4
$$
✔ Answer: $x = 4$
---
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. $\frac{x}{8} = \frac{10}{16}$
Cross multiply:
$$
x \cdot 16 = 8 \cdot 10 \\
16x = 80 \\
x = \frac{80}{16} = 5
$$
✔ Answer: $x = 5$
---
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. $\frac{x}{4} = \frac{9}{12}$
Cross multiply:
$$
x \cdot 12 = 4 \cdot 9 \\
12x = 36 \\
x = \frac{36}{12} = 3
$$
✔ Answer: $x = 3$
---
10. $\frac{1}{3} = \frac{3}{x}$
Cross multiply:
$$
1 \cdot x = 3 \cdot 3 \\
x = 9
$$
✔ Answer: $x = 9$
---
11. $\frac{x}{2} = \frac{4}{8}$
Cross multiply:
$$
x \cdot 8 = 2 \cdot 4 \\
8x = 8 \\
x = 1
$$
✔ 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 |
| 6 | 4 |
| 7 | 5 |
| 8 | 1 |
| 9 | 3 |
| 10 | 9 |
| 11 | 1 |
| 12 | 1 |
---
🔍 Summary:
All problems were solved using
cross multiplication, where we multiplied diagonally and solved for the unknown variable. This method works because in a proportion, the product of the means equals the product of the extremes.
Let me know if you'd like these checked with simplification or visual explanations!
Parent Tip: Review the logic above to help your child master the concept of 6th grade proportions worksheet.
