1. **Stating the problem:** We need to prove the equation $$H = \frac{h}{a} \times (a + b)$$. 2. **Understanding the equation:** This equation expresses $H$ as a product of the fraction $\frac{h}{a}$ and the sum $(a + b)$. 3. **Proof by algebraic manipulation:** Start with the right-hand side (RHS): $$\frac{h}{a} \times (a + b) = \frac{h}{a} \times a + \frac{h}{a} \times b$$ 4. Simplify each term: $$= h + \frac{h}{a} b$$ 5. The equation states $H$ equals this expression, so: $$H = h + \frac{h}{a} b$$ 6. This shows $H$ is $h$ plus a fraction of $h$ scaled by $b$ over $a$. 7. **Interpretation:** If $H$ is defined as such, the equation holds by distributive property of multiplication over addition. **Final answer:** The equation $$H = \frac{h}{a} \times (a + b)$$ is true by the distributive property and algebraic simplification.