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 multiplying the top of one fraction by the bottom of the other, and setting them equal to each other. Then, divide to find the missing number.

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: $27 \cdot x = 21 \cdot 18$
* Simplify: $27x = 378$
* 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: $45w = 55440$
* Divide by 45: $w = \frac{55440}{45}$
* $w = 1232$

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: $21000 = 1050p$
* Divide by 1050: $p = \frac{21000}{1050}$
* $p = 20$

11. $\frac{a}{1134} = \frac{27}{729}$
* Cross-multiply: $a \cdot 729 = 1134 \cdot 27$
* Simplify: $729a = 30618$
* Divide by 729: $a = \frac{30618}{729}$
* $a = 42$

12. $\frac{40}{65} = \frac{z}{104}$
* Cross-multiply: $40 \cdot 104 = 65 \cdot z$
* Simplify: $4160 = 65z$
* Divide by 65: $z = \frac{4160}{65}$
* $z = 64$

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

15. $\frac{32.5}{25} = \frac{97.5}{q}$
* Cross-multiply: $32.5 \cdot q = 25 \cdot 97.5$
* Simplify: $32.5q = 2437.5$
* Divide by 32.5: $q = \frac{2437.5}{32.5}$
* $q = 75$

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 = 1232
9. j = 2
10. p = 20
11. a = 42
12. z = 64
13. y = 4.5
14. r = 51.2
15. q = 75