8-(3-1/4)+1 1/6

To solve the expression \( 8 - (3 - \frac{1}{4}) + 1 \frac{1}{6} \), let's break it down step by step.

1. Convert mixed number to an improper fraction:
   \( 1 \frac{1}{6} = \frac{6 \cdot 1 + 1}{6} = \frac{7}{6} \)

2. Substitute the mixed number back into the expression:
   The expression now looks like:
   \( 8 - (3 - \frac{1}{4}) + \frac{7}{6} \)

3. Evaluate the parenthesis:
   Inside the parentheses, we calculate:
   \( 3 - \frac{1}{4} \)
   To do this, convert \( 3 \) to a fraction with a denominator of 4:
   \( 3 = \frac{12}{4} \)
   Thus,
   \( 3 - \frac{1}{4} = \frac{12}{4} - \frac{1}{4} = \frac{11}{4} \)

4. Substitute back into the expression:
   Now the expression is:
   \( 8 - \frac{11}{4} + \frac{7}{6} \)

5. Convert \( 8 \) to a fraction with a common denominator (LCM of 4 and 6 is 12):
   \( 8 = \frac{96}{12} \)
   \( \frac{11}{4} = \frac{33}{12} \) (by multiplying the numerator and denominator by 3)
   \( \frac{7}{6} = \frac{14}{12} \) (by multiplying the numerator and denominator by 2)

6. Substitute everything back into the expression:
   The expression now reads:
   \( \frac{96}{12} - \frac{33}{12} + \frac{14}{12} \)

7. Combine the fractions:
   \( \frac{96 - 33 + 14}{12} = \frac{96 - 33 + 14}{12} = \frac{77}{12} \)

8. Convert the improper fraction to a mixed number:
   \( \frac{77}{12} = 6 \frac{5}{12} \)

So the result of the expression \( 8 - (3 - \frac{1}{4}) + 1 \frac{1}{6} \) is:
\[ 6 \frac{5}{12} \]