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: \[ 6 \frac{5}{12} \]