Solving Proportions Worksheet - Free Printable

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

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

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

3. $\frac{5}{2} = \frac{2}{x}$
* Cross-multiply: $5 \cdot x = 2 \cdot 2$
* Simplify: $5x = 4$
* Divide by 5: $x = \frac{4}{5}$
* $x = 0.8$

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

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

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

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

8. $\frac{45}{792} = \frac{70}{w}$
* Cross-multiply: $45 \cdot w = 792 \cdot 70$
* Simplify: $45w = 55,440$
* Divide by 45: $w = \frac{55,440}{45}$
* $w = 1,232$

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

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

11. $\frac{a}{1134} = \frac{27}{729}$
* Cross-multiply: $a \cdot 729 = 1134 \cdot 27$
* Simplify: $729a = 30,618$
* Divide by 729: $a = \frac{30,618}{729}$
* $a = 42$

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

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

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

15. $\frac{32.5}{25} = \frac{97.5}{q}$
* Cross-multiply: $32.5 \cdot q = 25 \cdot 97.5$
* Simplify: $32.5q = 2,437.5$
* Divide by 32.5: $q = \frac{2,437.5}{32.5}$
* $q = 75$

Final Answer:
1. x = 22.5
2. x = 2.4
3. x = 0.8
4. x = 14
5. y = 28
6. b = 6
7. h = 42
8. w = 1,232
9. j = 2
10. p = 20
11. a = 42
12. x = 64
13. y = 4.5
14. y = 51.2
15. q = 75