Mixed Number Sum 560D23

1. **State the problem:** We need to calculate the sum of the mixed numbers $1 \frac{5}{12}$ and $2 \frac{2}{3}$ and express the answer as a mixed number in simplest form. 2. **Convert mixed numbers to improper fractions:** - $1 \frac{5}{12} = \frac{1 \times 12 + 5}{12} = \frac{12 + 5}{12} = \frac{17}{12}$ - $2 \frac{2}{3} = \frac{2 \times 3 + 2}{3} = \frac{6 + 2}{3} = \frac{8}{3}$ 3. **Find a common denominator:** - The denominators are $12$ and $3$. - The least common denominator (LCD) is $12$. 4. **Convert fractions to have the LCD:** - $\frac{17}{12}$ stays the same. - $\frac{8}{3} = \frac{8 \times 4}{3 \times 4} = \frac{32}{12}$ 5. **Add the fractions:** $$\frac{17}{12} + \frac{32}{12} = \frac{17 + 32}{12} = \frac{49}{12}$$ 6. **Convert the improper fraction back to a mixed number:** - Divide $49$ by $12$: $49 \div 12 = 4$ remainder $1$. - So, $\frac{49}{12} = 4 \frac{1}{12}$. 7. **Simplify the fraction if possible:** - $\frac{1}{12}$ is already in simplest form. **Final answer:** $4 \frac{1}{12}$