4 13/21-2 3/21+6 8/21

To solve the expression \( 4 \frac{13}{21} - 2 \frac{3}{21} + 6 \frac{8}{21} \), we can first convert the mixed numbers to improper fractions.

1. Convert each mixed number to an improper fraction:

   • \( 4 \frac{13}{21} = \frac{4 \times 21 + 13}{21} = \frac{84 + 13}{21} = \frac{97}{21} \)
   • \( 2 \frac{3}{21} = \frac{2 \times 21 + 3}{21} = \frac{42 + 3}{21} = \frac{45}{21} \)
   • \( 6 \frac{8}{21} = \frac{6 \times 21 + 8}{21} = \frac{126 + 8}{21} = \frac{134}{21} \)

2. Now substitute these fractions back into the expression: \[ \frac{97}{21} - \frac{45}{21} + \frac{134}{21} \]

3. Combine the fractions: \[ \frac{97 - 45 + 134}{21} = \frac{186}{21} \]

4. Simplify the fraction \( \frac{186}{21} \). Both the numerator and denominator can be divided by 3: \[ \frac{186 \div 3}{21 \div 3} = \frac{62}{7} \]

5. Convert back to a mixed number if needed: \( \frac{62}{7} = 8 \frac{6}{7} \) (since \( 62 \div 7 = 8 \) with a remainder of 6)

The final answer is: \[ 8 \frac{6}{7} \]