First, let's convert both mixed numbers into improper fractions.
For \(8 \frac{1}{2}\):
- The whole number part is 8, which is \(8 \times 2 = 16\).
- Adding the numerator 1 gives \(16 + 1 = 17\).
- Thus, \(8 \frac{1}{2} = \frac{17}{2}\).
For \(6 \frac{1}{3}\):
- The whole number part is 6, which is \(6 \times 3 = 18\).
- Adding the numerator 1 gives \(18 + 1 = 19\).
- Thus, \(6 \frac{1}{3} = \frac{19}{3}\).
Now we need to perform the subtraction: \[ 8 \frac{1}{2} - 6 \frac{1}{3} = \frac{17}{2} - \frac{19}{3} \]
To subtract these fractions, we need a common denominator. The least common multiple of 2 and 3 is 6.
Now convert each fraction to have a denominator of 6:
- For \(\frac{17}{2}\), multiply the numerator and denominator by 3: \[ \frac{17}{2} = \frac{17 \times 3}{2 \times 3} = \frac{51}{6} \]
- For \(\frac{19}{3}\), multiply the numerator and denominator by 2: \[ \frac{19}{3} = \frac{19 \times 2}{3 \times 2} = \frac{38}{6} \]
Now we can perform the subtraction: \[ \frac{51}{6} - \frac{38}{6} = \frac{51 - 38}{6} = \frac{13}{6} \]
Thus, the answer in mixed number form is: \[ 2 \frac{1}{6} \]
The numerator of the result \(\frac{13}{6}\) is 13.
So, the answer for the numerator is: \[ \boxed{13} \]
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