To simplify and solve the expression \(-\frac{3}{5} + \left(-\frac{8}{2}\right)\), follow these steps:
1. Identify the fractions: We have two fractions to work with: \(-\frac{3}{5}\) and \(-\frac{8}{2}\).
2. Evaluate \(-\frac{8}{2}\): Simplify \(-\frac{8}{2}\) by performing the division:
[tex]\[
-\frac{8}{2} = -4
\][/tex]
3. Rewrite the expression: Now the expression becomes:
[tex]\[
-\frac{3}{5} + (-4)
\][/tex]
4. Interpret the addition of a negative number: Adding a negative number is the same as subtracting:
[tex]\[
-\frac{3}{5} - 4
\][/tex]
5. Convert \(-4\) to a fraction with the same denominator as \(-\frac{3}{5}\):
- The common denominator is 5.
- Convert \(-4\) to a fraction with the denominator of 5:
[tex]\[
-4 = -\frac{4 \times 5}{1 \times 5} = -\frac{20}{5}
\][/tex]
6. Rewrite the expression with common denominators:
[tex]\[
-\frac{3}{5} - \frac{20}{5}
\][/tex]
7. Combine the fractions: Since the denominators are the same, combine the numerators:
[tex]\[
-\frac{3 + 20}{5}
\][/tex]
8. Simplify the combined fraction:
[tex]\[
-\frac{3 + 20}{5} = -\frac{23}{5}
\][/tex]
Thus, \(-\frac{3}{5} + \left(-\frac{8}{2}\right) = -\frac{23}{5}\).
Verifying with the decimal result, \(-0.6 + (-4.0) = -4.6\), this matches with \(-\frac{23}{5}\) in its decimal form, confirming the correctness of our calculation:
[tex]\[
-\frac{23}{5} = -4.6
\][/tex]
Therefore, the simplest form of the expression is [tex]\(-\frac{23}{5}\)[/tex].
