1. **Stating the problem:** We need to find the missing numbers in the equivalent fractions given: a) $\frac{3}{5} = \frac{12}{\square}$ b) $\frac{4}{10} = \frac{\square}{60}$ c) $\frac{6}{77} = \frac{42}{\square}$ d) $\frac{\square}{9} = \frac{36}{\square}$ 2. **Formula and rule:** Equivalent fractions satisfy the property: $$\frac{a}{b} = \frac{c}{d} \implies a \times d = b \times c$$ This means the cross products are equal. 3. **Solve a):** Given $\frac{3}{5} = \frac{12}{x}$, cross multiply: $$3 \times x = 5 \times 12$$ $$3x = 60$$ Divide both sides by 3: $$\cancel{3}x = \frac{60}{\cancel{3}}$$ $$x = 20$$ 4. **Solve b):** Given $\frac{4}{10} = \frac{y}{60}$, cross multiply: $$4 \times 60 = 10 \times y$$ $$240 = 10y$$ Divide both sides by 10: $$\frac{240}{\cancel{10}} = \cancel{10}y$$ $$24 = y$$ 5. **Solve c):** Given $\frac{6}{77} = \frac{42}{z}$, cross multiply: $$6 \times z = 77 \times 42$$ Calculate $77 \times 42$: $$77 \times 42 = 3234$$ So: $$6z = 3234$$ Divide both sides by 6: $$\cancel{6}z = \frac{3234}{\cancel{6}}$$ $$z = 539$$ 6. **Solve d):** Given $\frac{x}{9} = \frac{36}{w}$, cross multiply: $$x \times w = 9 \times 36$$ $$xw = 324$$ We need to find two numbers $x$ and $w$ such that $\frac{x}{9} = \frac{36}{w}$. Notice $\frac{36}{w} = \frac{x}{9}$ implies $\frac{x}{9} = \frac{36}{w}$. Try to express $x$ in terms of $w$: $$x = \frac{9 \times 36}{w} = \frac{324}{w}$$ To have both $x$ and $w$ integers, pick $w$ dividing 324. For example, if $w=18$, then: $$x = \frac{324}{18} = 18$$ Check equivalence: $$\frac{18}{9} = 2, \quad \frac{36}{18} = 2$$ So one solution is $x=18$, $w=18$. 7. **Final answers:** a) $20$ b) $24$ c) $539$ d) $x=18$, $w=18$ (one possible pair)