We need to evaluate the expression $ -\frac{3}{4} + 1\frac{5}{8} $. This involves adding a negative fraction to a mixed number.

1. Problem Description

We need to evaluate the expression $-\frac{3}{4} + 1\frac{5}{8}$. This involves adding a negative fraction to a mixed number.

2. Solution Steps

First, convert the mixed number $1\frac{5}{8}$ to an improper fraction:

$1\frac{5}{8} = \frac{1 \times 8 + 5}{8} = \frac{8+5}{8} = \frac{13}{8}$

Now, we have to calculate

$-\frac{3}{4} + \frac{13}{8}$

To add these fractions, we need a common denominator. The least common multiple of 4 and 8 is

8. So, we rewrite $ -\frac{3}{4}$ with a denominator of 8:

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

Now we can add the fractions:

$-\frac{6}{8} + \frac{13}{8} = \frac{-6 + 13}{8} = \frac{7}{8}$

3. Final Answer

$\frac{7}{8}$