Fraction Addition Ec3446

1. **State the problem:** We need to add $\frac{1}{4}$ and multiply by $\frac{1}{8}$. The problem can be interpreted as either $(\frac{1}{4} + x) \times \frac{1}{8}$ or simply adding $\frac{1}{4}$ and multiplying $\frac{1}{8}$, but since no other number is given, we assume the operation is $\frac{1}{4} + \frac{1}{8}$. 2. **Show the formula:** To add fractions, use the formula $$\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$$ where $a=1$, $b=4$, $c=1$, and $d=8$. 3. **Calculate the sum:** $$\frac{1}{4} + \frac{1}{8} = \frac{1 \times 8 + 1 \times 4}{4 \times 8} = \frac{8 + 4}{32} = \frac{12}{32}$$ 4. **Simplify the fraction:** $$\frac{12}{32} = \frac{\cancel{12}^{3} \times 4}{\cancel{32}^{8} \times 4} = \frac{3}{8}$$ 5. **Final answer:** The sum of $\frac{1}{4}$ and $\frac{1}{8}$ is $\frac{3}{8}$.