To evaluate the expression [tex]\(-\frac{2}{5} + \frac{1}{40}\)[/tex] and write the answer in its simplest form, follow these steps:
1. Convert the fractions to have a common denominator:
- The denominators are 5 and 40.
- Find the least common multiple (LCM) of 5 and 40. The LCM is 40.
- Rewrite [tex]\(-\frac{2}{5}\)[/tex] with the denominator 40.
[tex]\[
-\frac{2}{5} = -\frac{2 \times 8}{5 \times 8} = -\frac{16}{40}
\][/tex]
2. Rewrite the expression with a common denominator:
[tex]\[
-\frac{2}{5} + \frac{1}{40} = -\frac{16}{40} + \frac{1}{40}
\][/tex]
3. Add the fractions:
- Since the denominators are the same, you can add the numerators directly.
[tex]\[
-\frac{16}{40} + \frac{1}{40} = \frac{-16 + 1}{40} = \frac{-15}{40}
\][/tex]
4. Simplify the fraction:
- Find the greatest common divisor (GCD) of 15 and 40. The GCD is 5.
- Divide the numerator and the denominator by their GCD.
[tex]\[
\frac{-15}{40} = \frac{-15 \div 5}{40 \div 5} = \frac{-3}{8}
\][/tex]
Therefore, the simplified form of the expression [tex]\(-\frac{2}{5} + \frac{1}{40}\)[/tex] is [tex]\(\frac{-3}{8}\)[/tex].
