Math worksheet for solving proportion equations with variables.

Here are the step-by-step solutions for each proportion problem. To solve these, we use cross-multiplication: multiply the top of one fraction by the bottom of the other, and set them equal to each other. Then, divide to find the missing number.

a) $\frac{40}{24} = \frac{20}{a}$
1. Cross-multiply: $40 \times a = 24 \times 20$
2. Calculate: $40a = 480$
3. Divide by 40: $a = 480 / 40$
4. Result: 12

b) $\frac{33}{a} = \frac{11}{16}$
1. Cross-multiply: $33 \times 16 = 11 \times a$
2. Calculate: $528 = 11a$
3. Divide by 11: $a = 528 / 11$
4. Result: 48

c) $\frac{20}{b} = \frac{40}{26}$
1. Cross-multiply: $20 \times 26 = 40 \times b$
2. Calculate: $520 = 40b$
3. Divide by 40: $b = 520 / 40$
4. Result: 13

d) $\frac{10}{8} = \frac{b}{24}$
1. Cross-multiply: $10 \times 24 = 8 \times b$
2. Calculate: $240 = 8b$
3. Divide by 8: $b = 240 / 8$
4. Result: 30

e) $\frac{35}{a} = \frac{7}{2}$
1. Cross-multiply: $35 \times 2 = 7 \times a$
2. Calculate: $70 = 7a$
3. Divide by 7: $a = 70 / 7$
4. Result: 10

f) $\frac{44}{c} = \frac{22}{94}$
1. Cross-multiply: $44 \times 94 = 22 \times c$
2. Calculate: $4136 = 22c$
3. Divide by 22: $c = 4136 / 22$
4. Result: 188

g) $\frac{x}{6} = \frac{22}{44}$
1. Cross-multiply: $x \times 44 = 6 \times 22$
2. Calculate: $44x = 132$
3. Divide by 44: $x = 132 / 44$
4. Result: 3

h) $\frac{y}{10} = \frac{36}{20}$
1. Cross-multiply: $y \times 20 = 10 \times 36$
2. Calculate: $20y = 360$
3. Divide by 20: $y = 360 / 20$
4. Result: 18

i) $\frac{15}{45} = \frac{9}{y}$
1. Cross-multiply: $15 \times y = 45 \times 9$
2. Calculate: $15y = 405$
3. Divide by 15: $y = 405 / 15$
4. Result: 27

j) $\frac{40}{25} = \frac{b}{20}$
1. Cross-multiply: $40 \times 20 = 25 \times b$
2. Calculate: $800 = 25b$
3. Divide by 25: $b = 800 / 25$
4. Result: 32

k) $\frac{z}{5} = \frac{20}{25}$
1. Cross-multiply: $z \times 25 = 5 \times 20$
2. Calculate: $25z = 100$
3. Divide by 25: $z = 100 / 25$
4. Result: 4

l) $\frac{14}{20} = \frac{28}{y}$
1. Cross-multiply: $14 \times y = 20 \times 28$
2. Calculate: $14y = 560$
3. Divide by 14: $y = 560 / 14$
4. Result: 40

Final Answer:
a = 12
b = 48
b = 13
b = 30
a = 10
c = 188
x = 3
y = 18
y = 27
b = 32
z = 4
y = 40