This proportions worksheet provides structured practice for solving equations with fractions and finding unknown variables.

Let's solve each proportion step by step using cross-multiplication. The rule for solving proportions is:

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

---

a) $\frac{40}{24} = \frac{20}{a}$

Cross-multiply:
$40 \cdot a = 24 \cdot 20$
$40a = 480$
$a = \frac{480}{40} = 12$

✔ a = 12

---

b) $\frac{33}{a} = \frac{11}{16}$

Cross-multiply:
$33 \cdot 16 = 11 \cdot a$
$528 = 11a$
$a = \frac{528}{11} = 48$

✔ a = 48

---

c) $\frac{20}{b} = \frac{40}{26}$

Cross-multiply:
$20 \cdot 26 = 40 \cdot b$
$520 = 40b$
$b = \frac{520}{40} = 13$

✔ b = 13

---

d) $\frac{10}{8} = \frac{b}{24}$

Cross-multiply:
$10 \cdot 24 = 8 \cdot b$
$240 = 8b$
$b = \frac{240}{8} = 30$

✔ b = 30

---

e) $\frac{35}{a} = \frac{7}{2}$

Cross-multiply:
$35 \cdot 2 = 7 \cdot a$
$70 = 7a$
$a = \frac{70}{7} = 10$

✔ a = 10

---

f) $\frac{44}{c} = \frac{22}{94}$

Cross-multiply:
$44 \cdot 94 = 22 \cdot c$
$4136 = 22c$
$c = \frac{4136}{22} = 188$

✔ c = 188

---

g) $\frac{x}{6} = \frac{22}{44}$

Simplify the right side: $\frac{22}{44} = \frac{1}{2}$
So: $\frac{x}{6} = \frac{1}{2}$

Cross-multiply:
$2x = 6$
$x = 3$

✔ x = 3

---

h) $\frac{y}{10} = \frac{36}{20}$

Simplify: $\frac{36}{20} = \frac{9}{5}$
So: $\frac{y}{10} = \frac{9}{5}$

Cross-multiply:
$5y = 90$
$y = 18$

✔ y = 18

---

i) $\frac{15}{45} = \frac{9}{y}$

Simplify left side: $\frac{15}{45} = \frac{1}{3}$
So: $\frac{1}{3} = \frac{9}{y}$

Cross-multiply:
$1 \cdot y = 3 \cdot 9$
$y = 27$

✔ y = 27

---

j) $\frac{40}{25} = \frac{b}{20}$

Simplify left: $\frac{40}{25} = \frac{8}{5}$
So: $\frac{8}{5} = \frac{b}{20}$

Cross-multiply:
$8 \cdot 20 = 5 \cdot b$
$160 = 5b$
$b = \frac{160}{5} = 32$

✔ b = 32

---

k) $\frac{z}{5} = \frac{20}{25}$

Simplify right: $\frac{20}{25} = \frac{4}{5}$
So: $\frac{z}{5} = \frac{4}{5}$

Multiply both sides by 5:
$z = 4$

✔ z = 4

---

l) $\frac{14}{20} = \frac{28}{y}$

Simplify left: $\frac{14}{20} = \frac{7}{10}$
So: $\frac{7}{10} = \frac{28}{y}$

Cross-multiply:
$7y = 280$
$y = \frac{280}{7} = 40$

✔ y = 40

---

✔ Final Answers:

| Problem | Answer |
|--------|--------|
| a | 12 |
| b | 48 |
| c | 13 |
| d | 30 |
| e | 10 |
| f | 188 |
| g | 3 |
| h | 18 |
| i | 27 |
| j | 32 |
| k | 4 |
| l | 40 |

Let me know if you'd like a visual explanation or help with any specific one!