1. **Stating the problem:** Four children share $\frac{3}{8}$ of a big cake equally. We need to find what fraction of the cake each child gets. 2. **Formula used:** When a quantity is shared equally among a number of people, each person gets the total quantity divided by the number of people. Mathematically, if $Q$ is the total quantity and $n$ is the number of people, each gets $\frac{Q}{n}$. 3. **Applying the formula:** Here, $Q = \frac{3}{8}$ and $n = 4$. So each child gets: $$\frac{3}{8} \div 4 = \frac{3}{8} \times \frac{1}{4}$$ 4. **Simplifying:** $$\frac{3}{8} \times \frac{1}{4} = \frac{3 \times 1}{8 \times 4} = \frac{3}{32}$$ 5. **Answer:** Each child gets $\frac{3}{32}$ of the cake. This means the cake is divided into 32 equal parts, and each child receives 3 of those parts.