1. Stating the problem: Solve the equation $$\frac{8}{10} = \frac{w}{5}$$ for $w$. 2. Use the cross-multiplication rule for proportions: $$a/b = c/d \implies ad = bc$$. 3. Apply cross multiplication: $$8 \times 5 = 10 \times w$$ 4. Simplify both sides: $$40 = 10w$$ 5. Divide both sides by 10 to isolate $w$: $$\frac{40}{\cancel{10}} = \frac{10w}{\cancel{10}}$$ 6. Simplify the division: $$4 = w$$ 7. Final answer: $$w = 4$$