Solving Proportions Worksheet - Free Printable

Let's solve each proportion step by step using cross-multiplication. The principle is:

> If $\frac{a}{b} = \frac{c}{d}$, then $a \cdot d = b \cdot c$

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1) $\frac{32}{8} = \frac{16}{h}$

Cross-multiply:
$$
32 \cdot h = 8 \cdot 16 \\
32h = 128 \\
h = \frac{128}{32} = 4
$$

✔ Answer: $h = 4$

---

2) $\frac{6}{b} = \frac{2}{3}$

Cross-multiply:
$$
6 \cdot 3 = 2 \cdot b \\
18 = 2b \\
b = \frac{18}{2} = 9
$$

✔ Answer: $b = 9$

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3) $\frac{7}{14} = \frac{21}{2x}$

Simplify left side: $\frac{7}{14} = \frac{1}{2}$

So:
$$
\frac{1}{2} = \frac{21}{2x}
$$

Cross-multiply:
$$
1 \cdot 2x = 2 \cdot 21 \\
2x = 42 \\
x = 21
$$

✔ Answer: $x = 21$

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4) $\frac{10}{15} = \frac{2z}{3}$

Simplify left side: $\frac{10}{15} = \frac{2}{3}$

So:
$$
\frac{2}{3} = \frac{2z}{3}
$$

Multiply both sides by 3:
$$
2 = 2z \Rightarrow z = 1
$$

✔ Answer: $z = 1$

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5) $\frac{v}{66} = \frac{18}{33}$

Cross-multiply:
$$
v \cdot 33 = 66 \cdot 18 \\
33v = 1188 \\
v = \frac{1188}{33} = 36
$$

✔ Answer: $v = 36$

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6) $\frac{60}{k} = \frac{15}{21}$

Simplify right side: $\frac{15}{21} = \frac{5}{7}$

So:
$$
\frac{60}{k} = \frac{5}{7}
$$

Cross-multiply:
$$
60 \cdot 7 = 5 \cdot k \\
420 = 5k \\
k = \frac{420}{5} = 84
$$

✔ Answer: $k = 84$

---

7) $\frac{a}{7} = \frac{8}{28}$

Simplify right side: $\frac{8}{28} = \frac{2}{7}$

So:
$$
\frac{a}{7} = \frac{2}{7}
\Rightarrow a = 2
$$

✔ Answer: $a = 2$

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8) $\frac{3}{4} = \frac{5d}{20}$

Simplify right side: $\frac{5d}{20} = \frac{d}{4}$

So:
$$
\frac{3}{4} = \frac{d}{4}
\Rightarrow d = 3
$$

✔ Answer: $d = 3$

---

9) $\frac{w}{18} = \frac{2}{9}$

Cross-multiply:
$$
w \cdot 9 = 18 \cdot 2 \\
9w = 36 \\
w = \frac{36}{9} = 4
$$

✔ Answer: $w = 4$

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10) $\frac{15}{s} = \frac{30}{10}$

Simplify right side: $\frac{30}{10} = 3$

So:
$$
\frac{15}{s} = 3 \Rightarrow s = \frac{15}{3} = 5
$$

✔ Answer: $s = 5$

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11) $\frac{4}{9} = \frac{12}{u}$

Cross-multiply:
$$
4 \cdot u = 9 \cdot 12 \\
4u = 108 \\
u = \frac{108}{4} = 27
$$

✔ Answer: $u = 27$

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12) $\frac{3t}{15} = \frac{36}{60}$

Simplify both sides:

Left: $\frac{3t}{15} = \frac{t}{5}$

Right: $\frac{36}{60} = \frac{3}{5}$

So:
$$
\frac{t}{5} = \frac{3}{5} \Rightarrow t = 3
$$

✔ Answer: $t = 3$

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✔ Final Answers:

1) $h = 4$
2) $b = 9$
3) $x = 21$
4) $z = 1$
5) $v = 36$
6) $k = 84$
7) $a = 2$
8) $d = 3$
9) $w = 4$
10) $s = 5$
11) $u = 27$
12) $t = 3$

Let me know if you'd like this as a downloadable answer key!