Solving Proportions Worksheet - Free Printable

To solve each proportion, we will use the property of proportions that states:

\[
\frac{a}{b} = \frac{c}{d} \implies a \cdot d = b \cdot c
\]

This means we can cross-multiply to solve for the unknown variable. Let's solve each problem step by step.

---

Problem 1:

\[
\frac{4}{9} = \frac{10}{x}
\]

Cross-multiply:
\[
4 \cdot x = 9 \cdot 10
\]
\[
4x = 90
\]

Solve for \( x \):
\[
x = \frac{90}{4} = 22.5
\]

Answer:
\[
x = 22.5
\]

---

Problem 2:

\[
\frac{5}{2} = \frac{6}{x}
\]

Cross-multiply:
\[
5 \cdot x = 2 \cdot 6
\]
\[
5x = 12
\]

Solve for \( x \):
\[
x = \frac{12}{5} = 2.4
\]

Answer:
\[
x = 2.4
\]

---

Problem 3:

\[
\frac{5}{2} = \frac{2}{x}
\]

Cross-multiply:
\[
5 \cdot x = 2 \cdot 2
\]
\[
5x = 4
\]

Solve for \( x \):
\[
x = \frac{4}{5} = 0.8
\]

Answer:
\[
x = 0.8
\]

---

Problem 4:

\[
\frac{21}{27} = \frac{x}{18}
\]

Cross-multiply:
\[
21 \cdot 18 = 27 \cdot x
\]
\[
378 = 27x
\]

Solve for \( x \):
\[
x = \frac{378}{27} = 14
\]

Answer:
\[
x = 14
\]

---

Problem 5:

\[
\frac{15}{21} = \frac{20}{y}
\]

Cross-multiply:
\[
15 \cdot y = 21 \cdot 20
\]
\[
15y = 420
\]

Solve for \( y \):
\[
y = \frac{420}{15} = 28
\]

Answer:
\[
y = 28
\]

---

Problem 6:

\[
\frac{26}{b} = \frac{39}{9}
\]

Cross-multiply:
\[
26 \cdot 9 = 39 \cdot b
\]
\[
234 = 39b
\]

Solve for \( b \):
\[
b = \frac{234}{39} = 6
\]

Answer:
\[
b = 6
\]

---

Problem 7:

\[
\frac{h}{108} = \frac{7}{18}
\]

Cross-multiply:
\[
h \cdot 18 = 108 \cdot 7
\]
\[
18h = 756
\]

Solve for \( h \):
\[
h = \frac{756}{18} = 42
\]

Answer:
\[
h = 42
\]

---

Problem 8:

\[
\frac{45}{792} = \frac{70}{w}
\]

Cross-multiply:
\[
45 \cdot w = 792 \cdot 70
\]
\[
45w = 55440
\]

Solve for \( w \):
\[
w = \frac{55440}{45} = 1232
\]

Answer:
\[
w = 1232
\]

---

Problem 9:

\[
\frac{16}{120} = \frac{j}{15}
\]

Cross-multiply:
\[
16 \cdot 15 = 120 \cdot j
\]
\[
240 = 120j
\]

Solve for \( j \):
\[
j = \frac{240}{120} = 2
\]

Answer:
\[
j = 2
\]

---

Problem 10:

\[
\frac{350}{p} = \frac{1050}{60}
\]

Cross-multiply:
\[
350 \cdot 60 = 1050 \cdot p
\]
\[
21000 = 1050p
\]

Solve for \( p \):
\[
p = \frac{21000}{1050} = 20
\]

Answer:
\[
p = 20
\]

---

Problem 11:

\[
\frac{q}{1134} = \frac{27}{729}
\]

First, simplify the right-hand side:
\[
\frac{27}{729} = \frac{1}{27}
\]

So the equation becomes:
\[
\frac{q}{1134} = \frac{1}{27}
\]

Cross-multiply:
\[
q \cdot 27 = 1134 \cdot 1
\]
\[
27q = 1134
\]

Solve for \( q \):
\[
q = \frac{1134}{27} = 42
\]

Answer:
\[
q = 42
\]

---

Problem 12:

\[
\frac{40}{65} = \frac{x}{104}
\]

Cross-multiply:
\[
40 \cdot 104 = 65 \cdot x
\]
\[
4160 = 65x
\]

Solve for \( x \):
\[
x = \frac{4160}{65} = 64
\]

Answer:
\[
x = 64
\]

---

Problem 13:

\[
\frac{15}{y} = \frac{40}{32}
\]

First, simplify the right-hand side:
\[
\frac{40}{32} = \frac{5}{4}
\]

So the equation becomes:
\[
\frac{15}{y} = \frac{5}{4}
\]

Cross-multiply:
\[
15 \cdot 4 = 5 \cdot y
\]
\[
60 = 5y
\]

Solve for \( y \):
\[
y = \frac{60}{5} = 12
\]

Answer:
\[
y = 12
\]

---

Problem 14:

\[
\frac{y}{12} = \frac{16}{10}
\]

First, simplify the right-hand side:
\[
\frac{16}{10} = \frac{8}{5}
\]

So the equation becomes:
\[
\frac{y}{12} = \frac{8}{5}
\]

Cross-multiply:
\[
y \cdot 5 = 12 \cdot 8
\]
\[
5y = 96
\]

Solve for \( y \):
\[
y = \frac{96}{5} = 19.2
\]

Answer:
\[
y = 19.2
\]

---

Problem 15:

\[
\frac{32.5}{25} = \frac{97.5}{q}
\]

Cross-multiply:
\[
32.5 \cdot q = 25 \cdot 97.5
\]
\[
32.5q = 2437.5
\]

Solve for \( q \):
\[
q = \frac{2437.5}{32.5} = 75
\]

Answer:
\[
q = 75
\]

---

Final Answers:

\[
\boxed{
\begin{aligned}
1. & \ x = 22.5 \\
2. & \ x = 2.4 \\
3. & \ x = 0.8 \\
4. & \ x = 14 \\
5. & \ y = 28 \\
6. & \ b = 6 \\
7. & \ h = 42 \\
8. & \ w = 1232 \\
9. & \ j = 2 \\
10. & \ p = 20 \\
11. & \ q = 42 \\
12. & \ x = 64 \\
13. & \ y = 12 \\
14. & \ y = 19.2 \\
15. & \ q = 75 \\
\end{aligned}
}
\]