1. **State the problem:** Add the fractions $\frac{4}{6}$ and $\frac{4}{8}$. 2. **Formula:** To add fractions, use the formula $$\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$$ where $a$, $b$, $c$, and $d$ are integers and $b,d \neq 0$. 3. **Find a common denominator:** The denominators are 6 and 8. The least common denominator (LCD) is the least common multiple (LCM) of 6 and 8. - Prime factors: 6 = 2 \times 3, 8 = 2^3 - LCM = 2^3 \times 3 = 8 \times 3 = 24 4. **Rewrite each fraction with denominator 24:** $$\frac{4}{6} = \frac{4 \times 4}{6 \times 4} = \frac{16}{24}$$ $$\frac{4}{8} = \frac{4 \times 3}{8 \times 3} = \frac{12}{24}$$ 5. **Add the numerators:** $$\frac{16}{24} + \frac{12}{24} = \frac{16 + 12}{24} = \frac{28}{24}$$ 6. **Simplify the fraction:** - Find the greatest common divisor (GCD) of 28 and 24, which is 4. - Cancel common factors: $$\frac{\cancel{4} \times 7}{\cancel{4} \times 6} = \frac{7}{6}$$ 7. **Final answer:** $$\frac{4}{6} + \frac{4}{8} = \frac{7}{6}$$ which is an improper fraction and can also be written as $$1 \frac{1}{6}$$.