Solving Proportions Worksheet with 15 math problems to solve by showing work.

Here are the step-by-step solutions for each proportion on the worksheet. To solve a proportion, you can use cross-multiplication: multiply the top of one fraction by the bottom of the other, and set them equal to each other. Then, divide to find the missing variable.

1. $\frac{4}{9} = \frac{10}{x}$
* Cross-multiply: $4 \cdot x = 9 \cdot 10$
* Equation: $4x = 90$
* Divide by 4: $x = \frac{90}{4} = 22.5$

2. $\frac{5}{2} = \frac{6}{x}$
* Cross-multiply: $5 \cdot x = 2 \cdot 6$
* Equation: $5x = 12$
* Divide by 5: $x = \frac{12}{5} = 2.4$

3. $\frac{8}{2} = \frac{x}{7}$
* Simplify the left side first: $\frac{8}{2} = 4$
* Equation: $4 = \frac{x}{7}$
* Multiply by 7: $x = 4 \cdot 7 = 28$

4. $\frac{21}{27} = \frac{x}{18}$
* Cross-multiply: $21 \cdot 18 = 27 \cdot x$
* Calculate: $378 = 27x$
* Divide by 27: $x = \frac{378}{27} = 14$

5. $\frac{15}{21} = \frac{20}{y}$
* Cross-multiply: $15 \cdot y = 21 \cdot 20$
* Calculate: $15y = 420$
* Divide by 15: $y = \frac{420}{15} = 28$

6. $\frac{26}{b} = \frac{39}{9}$
* Cross-multiply: $26 \cdot 9 = b \cdot 39$
* Calculate: $234 = 39b$
* Divide by 39: $b = \frac{234}{39} = 6$

7. $\frac{n}{108} = \frac{7}{18}$
* Cross-multiply: $n \cdot 18 = 108 \cdot 7$
* Calculate: $18n = 756$
* Divide by 18: $n = \frac{756}{18} = 42$

8. $\frac{49}{792} = \frac{70}{w}$
* Cross-multiply: $49 \cdot w = 792 \cdot 70$
* Calculate: $49w = 55,440$
* Divide by 49: $w = \frac{55,440}{49} \approx 1131.43$ (rounded to two decimal places)

9. $\frac{16}{120} = \frac{j}{15}$
* Cross-multiply: $16 \cdot 15 = 120 \cdot j$
* Calculate: $240 = 120j$
* Divide by 120: $j = \frac{240}{120} = 2$

10. $\frac{350}{p} = \frac{1050}{60}$
* Cross-multiply: $350 \cdot 60 = p \cdot 1050$
* Calculate: $21,000 = 1050p$
* Divide by 1050: $p = \frac{21,000}{1050} = 20$

11. $\frac{a}{1134} = \frac{27}{729}$
* Cross-multiply: $a \cdot 729 = 1134 \cdot 27$
* Calculate: $729a = 30,618$
* Divide by 729: $a = \frac{30,618}{729} \approx 42$ (Exact calculation: $30618 / 729 = 42$)

12. $\frac{40}{65} = \frac{t}{104}$
* Cross-multiply: $40 \cdot 104 = 65 \cdot t$
* Calculate: $4,160 = 65t$
* Divide by 65: $t = \frac{4,160}{65} = 64$

13. $\frac{15}{y} = \frac{40}{12}$
* Cross-multiply: $15 \cdot 12 = y \cdot 40$
* Calculate: $180 = 40y$
* Divide by 40: $y = \frac{180}{40} = 4.5$

14. $\frac{y}{32} = \frac{16}{10}$
* Cross-multiply: $y \cdot 10 = 32 \cdot 16$
* Calculate: $10y = 512$
* Divide by 10: $y = \frac{512}{10} = 51.2$

15. $\frac{32.5}{25} = \frac{57.5}{q}$
* Cross-multiply: $32.5 \cdot q = 25 \cdot 57.5$
* Calculate: $32.5q = 1,437.5$
* Divide by 32.5: $q = \frac{1,437.5}{32.5} \approx 44.23$ (rounded to two decimal places)

Final Answer:
1. x = 22.5
2. x = 2.4
3. x = 28
4. x = 14
5. y = 28
6. b = 6
7. n = 42
8. w ≈ 1131.43
9. j = 2
10. p = 20
11. a = 42
12. t = 64
13. y = 4.5
14. y = 51.2
15. q ≈ 44.23