1. **State the problem:** Anna ate $\frac{1}{4}$ of the cake and her brother ate $\frac{2}{8}$ of the cake. We need to find how much of the cake was eaten altogether. 2. **Recall the formula:** To add fractions, they must have a common denominator. Then add the numerators and keep the denominator the same. 3. **Find a common denominator:** The denominators are 4 and 8. The least common denominator is 8. 4. **Convert $\frac{1}{4}$ to eighths:** $$\frac{1}{4} = \frac{1 \times 2}{4 \times 2} = \frac{2}{8}$$ 5. **Add the fractions:** $$\frac{2}{8} + \frac{2}{8} = \frac{2+2}{8} = \frac{4}{8}$$ 6. **Simplify the fraction:** $$\frac{4}{8} = \frac{\cancel{4}^2}{\cancel{8}^4} = \frac{1}{2}$$ 7. **Answer:** Altogether, $\frac{1}{2}$ of the cake was eaten.