1. **State the problem:** Solve the equation $\frac{K+k}{k} = 6$ for $K$. 2. **Understand the formula:** The equation is a fraction where the numerator is $K+k$ and the denominator is $k$. We want to isolate $K$. 3. **Multiply both sides by $k$ to eliminate the denominator:** $$\cancel{k} \times \frac{K+k}{\cancel{k}} = 6 \times k$$ which simplifies to $$K + k = 6k$$ 4. **Isolate $K$ by subtracting $k$ from both sides:** $$K + k - k = 6k - k$$ which simplifies to $$K = 5k$$ 5. **Final answer:** $$K = 5k$$ This means $K$ is five times $k$.