1. The problem is to add two mixed numbers: $4 \frac{4}{8}$ and $3 \frac{2}{6}$. 2. Convert each mixed number to an improper fraction. - For $4 \frac{4}{8}$, multiply the whole number (4) by the denominator (8) and add the numerator (4): $$4 \times 8 + 4 = 32 + 4 = 36$$ So, $4 \frac{4}{8} = \frac{36}{8}$. - For $3 \frac{2}{6}$, multiply the whole number (3) by the denominator (6) and add the numerator (2): $$3 \times 6 + 2 = 18 + 2 = 20$$ So, $3 \frac{2}{6} = \frac{20}{6}$. 3. Find a common denominator for the fractions $\frac{36}{8}$ and $\frac{20}{6}$. - The denominators are 8 and 6. - The least common denominator (LCD) of 8 and 6 is 24. 4. Convert each fraction to have the denominator 24. - For $\frac{36}{8}$, multiply numerator and denominator by 3: $$\frac{36 \times 3}{8 \times 3} = \frac{108}{24}$$ - For $\frac{20}{6}$, multiply numerator and denominator by 4: $$\frac{20 \times 4}{6 \times 4} = \frac{80}{24}$$ 5. Add the fractions: $$\frac{108}{24} + \frac{80}{24} = \frac{188}{24}$$ 6. Simplify the fraction $\frac{188}{24}$. - Both numerator and denominator can be divided by 4: $$\frac{188 \div 4}{24 \div 4} = \frac{47}{6}$$ 7. Convert the improper fraction back to a mixed number. - Divide 47 by 6: $$47 \div 6 = 7 \text{ remainder } 5$$ - So the mixed number is $7 \frac{5}{6}$. **Final answer:** $4 \frac{4}{8} + 3 \frac{2}{6} = 7 \frac{5}{6}$