Solve: -3 + (-1/2) + (3/8) + 5/8 - Adding Mixed Fractions and Negative Numbers

To solve the given problem of adding $-3 + (-\frac{1}{2}) + \frac{3}{8} + \frac{5}{8}$, we will use the following steps:

• Step 1: Calculate $\frac{3}{8} + \frac{5}{8}$
• Step 2: Subtract $-\frac{1}{2}$ from the result of step 1
• Step 3: Add the final result to $-3$

Now, let us work through each step:

Step 1: Calculate $\frac{3}{8} + \frac{5}{8}$. Since these fractions have the same denominator, we simply add their numerators: $\frac{3 + 5}{8} = \frac{8}{8} = 1$.

Step 2: Now we subtract $-\frac{1}{2}$ from 1. We can rewrite $1$ as $\frac{8}{8}$ and $-\frac{1}{2}$ as $-\frac{4}{8}$ (since their least common denominator is 8). So: $1 - \left(-\frac{1}{2}\right) = \frac{8}{8} - \left(-\frac{4}{8}\right) = \frac{8 + 4}{8} = \frac{12}{8} = \frac{3}{2}.$

Step 3: Finally, we add this result to $-3$. $-3$ can be expressed as $-\frac{6}{2}$ and $\frac{3}{2}$ remains the same: $-3 + \frac{3}{2} = -\frac{6}{2} + \frac{3}{2} = \frac{-6 + 3}{2} = \frac{-3}{2} = -\frac{5}{2}.$

Hence, the solution to the problem is $-\frac{5}{2}$.