We need to calculate the value of the expression: $1\frac{1}{2} - \frac{3}{4} + 2\frac{3}{8}$.

1. Problem Description

We need to calculate the value of the expression: $1\frac{1}{2} - \frac{3}{4} + 2\frac{3}{8}$.

2. Solution Steps

First, convert the mixed numbers to improper fractions:

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

$2\frac{3}{8} = \frac{2 \times 8 + 3}{8} = \frac{19}{8}$

Now, the expression becomes:

$\frac{3}{2} - \frac{3}{4} + \frac{19}{8}$

Next, find a common denominator for the fractions. The least common multiple of 2, 4, and 8 is

8. Convert each fraction to an equivalent fraction with a denominator of 8:

$\frac{3}{2} = \frac{3 \times 4}{2 \times 4} = \frac{12}{8}$

$\frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8}$

$\frac{19}{8}$ already has the desired denominator.

Substitute these equivalent fractions into the expression:

$\frac{12}{8} - \frac{6}{8} + \frac{19}{8}$

Now, perform the operations:

$\frac{12}{8} - \frac{6}{8} = \frac{12 - 6}{8} = \frac{6}{8}$

$\frac{6}{8} + \frac{19}{8} = \frac{6 + 19}{8} = \frac{25}{8}$

Finally, convert the improper fraction to a mixed number:

$\frac{25}{8} = 3\frac{1}{8}$ (since $25 = 3 \times 8 + 1$)

3. Final Answer

$3\frac{1}{8}$