A person distributes some items between four children. The first child gets $\frac{1}{2}$ of the total items and the second child gets $\frac{1}{4}$ of the first child's share. The third child gets $\frac{3}{4}$ of the first child's share. What fraction does the fourth child get?

Explanation

Let the total object = $x$ items received by the first child = $\frac{x}{2}$ items received by the second child = $\frac{x}{2} \times \frac{1}{4} = \frac{x}{8}$ items received by the third child = $\frac{x}{2} \times \frac{3}{4} = \frac{3x}{8}$ ∴ items received by the fourth child = $x - \left\{ \frac{x}{2} + \frac{x}{8} + \frac{3x}{8} \right\}$ = $x - \left\{ \frac{4x + x + 3x}{8} \right\} = \frac{8x - 8x}{8} = 0$ Therefore, the fourth child gets nothing.