1. Stated problem: Solve for $k$ in the equation $$\frac{3}{k} = \frac{4}{5}$$. 2. Formula and rule: To solve for $k$, we use cross multiplication which states that if $$\frac{a}{b} = \frac{c}{d}$$, then $$a \times d = b \times c$$. 3. Apply cross multiplication: $$3 \times 5 = k \times 4$$ 4. Simplify the multiplication: $$15 = 4k$$ 5. Solve for $k$ by dividing both sides by 4: $$k = \frac{15}{4}$$ 6. Show cancellation step: $$k = \frac{\cancel{15}}{\cancel{4}}$$ (no common factors to cancel, so fraction remains the same) 7. Final answer: $$k = \frac{15}{4}$$