We need to evaluate the following expression: $(\frac{1}{2}) + (\frac{2}{3}) - (-1\frac{1}{6})$

1. Problem Description

We need to evaluate the following expression:

$(\frac{1}{2}) + (\frac{2}{3}) - (-1\frac{1}{6})$

2. Solution Steps

First, we rewrite the expression without the parentheses and plus signs, remembering that subtracting a negative is the same as adding:

$\frac{1}{2} + \frac{2}{3} - (-1\frac{1}{6}) = \frac{1}{2} + \frac{2}{3} + 1\frac{1}{6}$

Next, we convert the mixed number $1\frac{1}{6}$ to an improper fraction:

$1\frac{1}{6} = \frac{1 \times 6 + 1}{6} = \frac{6+1}{6} = \frac{7}{6}$

So the expression becomes:

$\frac{1}{2} + \frac{2}{3} + \frac{7}{6}$

Now, we find a common denominator for the fractions. The least common multiple of 2, 3, and 6 is

6. We rewrite each fraction with a denominator of 6:

$\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}$

$\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}$

$\frac{7}{6}$ remains the same.

Now we can add the fractions:

$\frac{3}{6} + \frac{4}{6} + \frac{7}{6} = \frac{3+4+7}{6} = \frac{14}{6}$

Finally, we simplify the fraction. We can divide both the numerator and the denominator by their greatest common divisor, which is 2:

$\frac{14}{6} = \frac{14 \div 2}{6 \div 2} = \frac{7}{3}$

We can also convert this improper fraction to a mixed number:

$\frac{7}{3} = 2\frac{1}{3}$

3. Final Answer

$\frac{7}{3}$ or $2\frac{1}{3}$