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Evaluate the expression below and write your answer as a fraction in simplest form.

[tex]\[
-\frac{2}{5} + \frac{1}{40}
\][/tex]

Answer:

[tex]\[\square\][/tex]



Answer :

GinnyAnswer
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].

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