Solve the following proportion equations on this math worksheet.

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

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

We'll apply this to each problem.

---

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 right side: $\frac{22}{44} = \frac{1}{2}$

So:
$$
\frac{x}{6} = \frac{1}{2}
$$
Cross-multiply:
$$
2x = 6 \Rightarrow x = 3
$$
✔ x = 3

---

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

Simplify right side: $\frac{36}{20} = \frac{9}{5}$

So:
$$
\frac{y}{10} = \frac{9}{5}
$$
Cross-multiply:
$$
5y = 90 \Rightarrow y = 18
$$
✔ 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:
$$
1 \cdot y = 3 \cdot 9 \Rightarrow y = 27
$$
✔ y = 27

---

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

Simplify left side: $\frac{40}{25} = \frac{8}{5}$

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

---

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

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

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 side: $\frac{14}{20} = \frac{7}{10}$

So:
$$
\frac{7}{10} = \frac{28}{y}
$$
Cross-multiply:
$$
7y = 280 \Rightarrow y = 40
$$
✔ 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 these explained in another way or visualized!