Question

1/8 + -3 3/5 (fractions)

Answer 1

To add the fractions \( \frac{1}{8} \) and \( -3 \frac{3}{5} \), we first need to convert the mixed number into an improper fraction.

1. Convert \( -3 \frac{3}{5} \) into an improper fraction:
\[
-3 \frac{3}{5} = -\left(3 \times 5 + 3\right)/5 = -\left(15 + 3\right)/5 = -\frac{18}{5}
\]

2. Now we need to add \( \frac{1}{8} \) and \( -\frac{18}{5} \):
\[
\frac{1}{8} + \left(-\frac{18}{5}\right) = \frac{1}{8} - \frac{18}{5}
\]

3. To add these fractions, we need a common denominator. The least common multiple of 8 and 5 is 40.

4. Convert each fraction:
\[
\frac{1}{8} = \frac{1 \times 5}{8 \times 5} = \frac{5}{40}
\]
\[
-\frac{18}{5} = -\frac{18 \times 8}{5 \times 8} = -\frac{144}{40}
\]

5. Now add the fractions:
\[
\frac{5}{40} - \frac{144}{40} = \frac{5 - 144}{40} = \frac{-139}{40}
\]

The final result is:
\[
\frac{-139}{40}
\]
This can be expressed as a mixed number:
\[
-3 \frac{19}{40}
\]

So, \( \frac{1}{8} + -3 \frac{3}{5} = -\frac{139}{40} \) or \( -3 \frac{19}{40} \).