Fractions Subtraction of mixed numbers with different denominators and renaming Subtract. Write your answer as a mixed number in simplest form. \[ 9 \frac{3}{7}-\frac{1}{2} \]

Step 1 ：Understand the problem: We are asked to subtract a fraction from a mixed number. The mixed number is \(9 \frac{3}{7}\) and the fraction is \(\frac{1}{2}\).

Step 2 ：Convert the mixed number to an improper fraction: \(9 \frac{3}{7} = \frac{9*7 + 3}{7} = \frac{66}{7}\).

Step 3 ：Find a common denominator: The denominators of the two fractions are 7 and 2. The least common multiple of 7 and 2 is 14. So, we need to convert each fraction to an equivalent fraction with a denominator of 14. \(\frac{66}{7} = \frac{132}{14}\) and \(\frac{1}{2} = \frac{7}{14}\).

Step 4 ：Subtract the fractions: Now that the fractions have the same denominator, we can subtract them by subtracting the numerators: \(\frac{132}{14} - \frac{7}{14} = \frac{125}{14}\).

Step 5 ：Convert the improper fraction back to a mixed number: \(\frac{125}{14} = 8 \frac{13}{14}\).

Step 6 ：\(\boxed{8 \frac{13}{14}}\) is the final answer.