a) \( 1 \frac{4}{7}+3 \frac{1}{21} \)

To solve \( 1 \frac{4}{7}+3 \frac{1}{21} \), first convert the mixed numbers into improper fractions for easier addition. 1. Convert \( 1 \frac{4}{7} \) into an improper fraction: \[ 1 \frac{4}{7} = \frac{(1 \times 7) + 4}{7} = \frac{11}{7} \] 2. Convert \( 3 \frac{1}{21} \) into an improper fraction: \[ 3 \frac{1}{21} = \frac{(3 \times 21) + 1}{21} = \frac{64}{21} \] Now, we need a common denominator to add the two fractions. The least common multiple of 7 and 21 is 21. 3. Convert \( \frac{11}{7} \) to have a denominator of 21: \[ \frac{11}{7} = \frac{11 \times 3}{7 \times 3} = \frac{33}{21} \] 4. Now add the two fractions: \[ \frac{33}{21} + \frac{64}{21} = \frac{33 + 64}{21} = \frac{97}{21} \] Finally, convert \( \frac{97}{21} \) back to a mixed number: 5. Perform division: \[ 97 \div 21 = 4 \quad \text{(with a remainder of 13)} \] So, \( 4 \frac{13}{21} \) is the result. Thus, \( 1 \frac{4}{7} + 3 \frac{1}{21} = 4 \frac{13}{21} \).