Verify the distributive law for rational numbers. [Page No. 49]

The law says $p(q + r) = pq + pr$.

Check it with $p = \frac{1}{2}, q = \frac{1}{3}, r = \frac{1}{4}$.

$$\begin{aligned} \text{LHS} &= \frac{1}{2} \left( \frac{1}{3} + \frac{1}{4} \right) = \frac{1}{2} \left( \frac{7}{12} \right) \\ &= \frac{7}{24} \end{aligned}$$

$$\begin{aligned} \text{RHS} &= \left( \frac{1}{2} \times \frac{1}{3} \right) + \left( \frac{1}{2} \times \frac{1}{4} \right) \\ &= \frac{1}{6} + \frac{1}{8} \\ &= \frac{4}{24} + \frac{3}{24} \\ &= \frac{7}{24} \end{aligned}$$

Since $\text{LHS} = \text{RHS} = \frac{7}{24}$, the distributive law holds. (You can try other values of $p, q, r$ and it will always work.)