1. **State the problem:** Solve for the unknown in the proportion equations given. 2. **Recall the rule for proportions:** If $\frac{a}{b} = \frac{c}{d}$, then $a \times d = b \times c$. 3. **Solve each part:** **a)** $\frac{9}{14} = \frac{?}{42}$ Using cross multiplication: $$9 \times 42 = 14 \times ?$$ $$378 = 14?$$ Divide both sides by 14: $$\cancel{14}? = \frac{378}{\cancel{14}}$$ $$? = 27$$ **b)** $\frac{3}{?} = \frac{36}{60}$ Cross multiply: $$3 \times 60 = ? \times 36$$ $$180 = 36?$$ Divide both sides by 36: $$\cancel{36}? = \frac{180}{\cancel{36}}$$ $$? = 5$$ **c)** $\frac{72}{?} = \frac{3}{4}$ Cross multiply: $$72 \times 4 = 3 \times ?$$ $$288 = 3?$$ Divide both sides by 3: $$\cancel{3}? = \frac{288}{\cancel{3}}$$ $$? = 96$$ **d)** $\frac{19}{5} = \frac{57}{?}$ Cross multiply: $$19 \times ? = 5 \times 57$$ $$19? = 285$$ Divide both sides by 19: $$\cancel{19}? = \frac{285}{\cancel{19}}$$ $$? = 15$$ **e)** $\frac{?}{100} = \frac{21}{30}$ Cross multiply: $$? \times 30 = 21 \times 100$$ $$30? = 2100$$ Divide both sides by 30: $$\cancel{30}? = \frac{2100}{\cancel{30}}$$ $$? = 70$$ **f)** $\frac{4}{?} = \frac{44}{77}$ Cross multiply: $$4 \times 77 = ? \times 44$$ $$308 = 44?$$ Divide both sides by 44: $$\cancel{44}? = \frac{308}{\cancel{44}}$$ $$? = 7$$ **g)** $\frac{3}{?} = \frac{75}{500}$ Cross multiply: $$3 \times 500 = ? \times 75$$ $$1500 = 75?$$ Divide both sides by 75: $$\cancel{75}? = \frac{1500}{\cancel{75}}$$ $$? = 20$$ **h)** $\frac{24}{?} = \frac{3}{5}$ Cross multiply: $$24 \times 5 = 3 \times ?$$ $$120 = 3?$$ Divide both sides by 3: $$\cancel{3}? = \frac{120}{\cancel{3}}$$ $$? = 40$$ **Final answers:** a) 27 b) 5 c) 96 d) 15 e) 70 f) 7 g) 20 h) 40