Solve: -1/4 - (-1/8) + 1/6 | Mixed Fraction Operations

$-\frac{1}{4}-(-\frac{1}{8})+\frac{1}{6}=$

To solve this problem, we'll follow these steps:

• Step 1: Simplify the double negative in the expression.
• Step 2: Find a common denominator for the fractions.
• Step 3: Convert and add/subtract the fractions with the common denominator.

Now, let's work through each step:
Step 1: Simplify $-(-\frac{1}{8})$ to get $\frac{1}{8}$. Thus, the expression becomes $-\frac{1}{4} + \frac{1}{8} + \frac{1}{6}$.

Step 2: Find a common denominator for the fractions $-\frac{1}{4}$, $\frac{1}{8}$, and $\frac{1}{6}$.
The denominators are 4, 8, and 6. The least common multiple (LCM) of these numbers is 24.

Step 3: Convert each fraction to have the common denominator of 24:
$-\frac{1}{4} = -\frac{6}{24}$
$\frac{1}{8} = \frac{3}{24}$
$\frac{1}{6} = \frac{4}{24}$

Now, perform the addition and subtraction:
$-\frac{6}{24} + \frac{3}{24} + \frac{4}{24} = \left(-6 + 3 + 4\right)/24 = 1/24$.

Therefore, the solution to the problem is $\frac{1}{24}$.