To solve the expression \( 1 \frac{3}{4} - (-\frac{2}{3}) \), we first convert the mixed number \( 1 \frac{3}{4} \) to an improper fraction:
\[ 1 \frac{3}{4} = \frac{4 \times 1 + 3}{4} = \frac{4 + 3}{4} = \frac{7}{4} \]
Now the expression becomes:
\[ \frac{7}{4} - (-\frac{2}{3}) = \frac{7}{4} + \frac{2}{3} \]
Next, we need a common denominator to add the two fractions. The least common multiple of \( 4 \) and \( 3 \) is \( 12 \).
Now, convert each fraction:
\[ \frac{7}{4} = \frac{7 \times 3}{4 \times 3} = \frac{21}{12} \]
\[ \frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12} \]
Now we can add the two fractions:
\[ \frac{21}{12} + \frac{8}{12} = \frac{21 + 8}{12} = \frac{29}{12} \]
The final answer is:
\[ \frac{29}{12} \]
If you want to convert it back to a mixed number, it is:
\[ 2 \frac{5}{12} \]
So, \( 1 \frac{3}{4} - (-\frac{2}{3}) = \frac{29}{12} \) or \( 2 \frac{5}{12} \).