O Fracions Addition or subtraction of mixed numbers with different denominators... Add. Write your answer as a mixed number in simplest form. \[ 5 \frac{2}{3}+2 \frac{1}{7} \]

To add \( 5 \frac{2}{3} + 2 \frac{1}{7} \), first convert each mixed number to an improper fraction. For \( 5 \frac{2}{3} \), multiply \( 5 \) by \( 3 \) and add \( 2 \): \[ 5 \times 3 + 2 = 15 + 2 = 17 \] So, \( 5 \frac{2}{3} = \frac{17}{3} \). For \( 2 \frac{1}{7} \): \[ 2 \times 7 + 1 = 14 + 1 = 15 \] So, \( 2 \frac{1}{7} = \frac{15}{7} \). Next, find a common denominator for \( \frac{17}{3} \) and \( \frac{15}{7} \). The least common multiple of \( 3 \) and \( 7 \) is \( 21 \). Convert both fractions: \[ \frac{17}{3} = \frac{17 \times 7}{3 \times 7} = \frac{119}{21} \] \[ \frac{15}{7} = \frac{15 \times 3}{7 \times 3} = \frac{45}{21} \] Now, add the two fractions: \[ \frac{119}{21} + \frac{45}{21} = \frac{119 + 45}{21} = \frac{164}{21} \] Convert \( \frac{164}{21} \) back to a mixed number. Divide \( 164 \) by \( 21 \): \[ 164 \div 21 = 7 \quad \text{(remainder 17)} \] So, \( \frac{164}{21} = 7 \frac{17}{21} \). The answer is \( 7 \frac{17}{21} \).