Comprehensive worksheet featuring twelve proportion problems designed to help students practice solving for unknown variables.

To solve these proportions, we use a method called cross-multiplication.

When you have an equation like $\frac{A}{B} = \frac{C}{D}$, you multiply the top of one side by the bottom of the other side. So, $A \times D = B \times C$. Then, you solve for the missing letter.

Here are the step-by-step solutions for each problem:

1) $\frac{32}{8} = \frac{16}{h}$
* Cross-multiply: $32 \times h = 8 \times 16$
* Calculate: $32h = 128$
* Divide by 32: $h = 4$

2) $\frac{6}{b} = \frac{2}{3}$
* Cross-multiply: $6 \times 3 = b \times 2$
* Calculate: $18 = 2b$
* Divide by 2: $b = 9$

3) $\frac{7}{14} = \frac{21}{2x}$
* Cross-multiply: $7 \times 2x = 14 \times 21$
* Calculate: $14x = 294$
* Divide by 14: $x = 21$

4) $\frac{10}{15} = \frac{2z}{3}$
* Cross-multiply: $10 \times 3 = 15 \times 2z$
* Calculate: $30 = 30z$
* Divide by 30: $z = 1$

5) $\frac{v}{66} = \frac{18}{33}$
* Cross-multiply: $v \times 33 = 66 \times 18$
* Calculate: $33v = 1188$
* Divide by 33: $v = 36$

6) $\frac{60}{k} = \frac{15}{21}$
* Cross-multiply: $60 \times 21 = k \times 15$
* Calculate: $1260 = 15k$
* Divide by 15: $k = 84$

7) $\frac{a}{7} = \frac{8}{28}$
* Cross-multiply: $a \times 28 = 7 \times 8$
* Calculate: $28a = 56$
* Divide by 28: $a = 2$

8) $\frac{3}{4} = \frac{5d}{20}$
* Cross-multiply: $3 \times 20 = 4 \times 5d$
* Calculate: $60 = 20d$
* Divide by 20: $d = 3$

9) $\frac{w}{18} = \frac{2}{9}$
* Cross-multiply: $w \times 9 = 18 \times 2$
* Calculate: $9w = 36$
* Divide by 9: $w = 4$

10) $\frac{15}{s} = \frac{30}{10}$
* Cross-multiply: $15 \times 10 = s \times 30$
* Calculate: $150 = 30s$
* Divide by 30: $s = 5$

11) $\frac{4}{9} = \frac{12}{u}$
* Cross-multiply: $4 \times u = 9 \times 12$
* Calculate: $4u = 108$
* Divide by 4: $u = 27$

12) $\frac{3t}{15} = \frac{36}{60}$
* Cross-multiply: $3t \times 60 = 15 \times 36$
* Calculate: $180t = 540$
* Divide by 180: $t = 3$

Final Answer:
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