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To solve \( 4 \frac{2}{6} + 1 \frac{3}{5} \), first convert the mixed numbers into improper fractions. For \( 4 \frac{2}{6} \): \[ 4 \times 6 + 2 = 24 + 2 = 26 \Rightarrow \frac{26}{6} \] For \( 1 \frac{3}{5} \): \[ 1 \times 5 + 3 = 5 + 3 = 8 \Rightarrow \frac{8}{5} \] Now, we need a common denominator to add these two fractions. The least common multiple of 6 and 5 is 30. Convert \( \frac{26}{6} \) to have a denominator of 30: \[ \frac{26}{6} \times \frac{5}{5} = \frac{130}{30} \] Convert \( \frac{8}{5} \) to have a denominator of 30: \[ \frac{8}{5} \times \frac{6}{6} = \frac{48}{30} \] Now, we can add the two fractions: \[ \frac{130}{30} + \frac{48}{30} = \frac{178}{30} \] To simplify, divide both the numerator and the denominator by 2: \[ \frac{178 \div 2}{30 \div 2} = \frac{89}{15} \] To convert \( \frac{89}{15} \) back to a mixed number: 89 divided by 15 is 5 with a remainder of 14, so: \[ 5 \frac{14}{15} \] Thus, the final answer is: \[ 4 \frac{2}{6} + 1 \frac{3}{5} = 5 \frac{14}{15} \]
