(8) \( 2 \frac{5}{6}+3 \frac{7}{12}= \)

To solve the addition of mixed numbers \( 2 \frac{5}{6} + 3 \frac{7}{12} \), first convert each mixed number to an improper fraction. For \( 2 \frac{5}{6} \): Multiply the whole number 2 by the denominator 6, add the numerator 5: \( 2 \times 6 + 5 = 12 + 5 = 17 \) So, \( 2 \frac{5}{6} = \frac{17}{6} \). For \( 3 \frac{7}{12} \): Multiply the whole number 3 by the denominator 12, add the numerator 7: \( 3 \times 12 + 7 = 36 + 7 = 43 \) So, \( 3 \frac{7}{12} = \frac{43}{12} \). Next, find a common denominator to add the fractions. The least common multiple of 6 and 12 is 12. Convert \( \frac{17}{6} \) to twelfths: \( \frac{17}{6} = \frac{17 \times 2}{6 \times 2} = \frac{34}{12} \). Now add the two fractions: \( \frac{34}{12} + \frac{43}{12} = \frac{34 + 43}{12} = \frac{77}{12} \). Finally, convert \( \frac{77}{12} \) back to a mixed number: Divide 77 by 12, which goes 6 times (as \( 6 \times 12 = 72 \)), with a remainder of 5. So, \( \frac{77}{12} = 6 \frac{5}{12} \). The final answer is: \( 2 \frac{5}{6} + 3 \frac{7}{12} = 6 \frac{5}{12} \).