To solve the expression [tex]\(\left[\frac{-8}{9}+\frac{2}{9}\right] \div\left[\frac{6}{10}-\frac{5}{2}\right]\)[/tex], let's break it down into two parts: the numerator and the denominator.
#### Step-by-Step Solution:
1. Calculate the Numerator:
The numerator is [tex]\(\frac{-8}{9} + \frac{2}{9}\)[/tex].
Since these two fractions have a common denominator, we can combine them directly:
[tex]\[
\frac{-8}{9} + \frac{2}{9} = \frac{-8 + 2}{9} = \frac{-6}{9}
\][/tex]
Simplify [tex]\(\frac{-6}{9}\)[/tex]:
[tex]\[
\frac{-6}{9} = \frac{-2}{3}
\][/tex]
Converting to decimal form:
[tex]\[
\frac{-2}{3} \approx -0.6666666666666666
\][/tex]
2. Calculate the Denominator:
The denominator is [tex]\(\frac{6}{10} - \frac{5}{2}\)[/tex].
First, convert [tex]\(\frac{5}{2}\)[/tex] to have a common denominator with [tex]\(\frac{6}{10}\)[/tex]. The common denominator here is 10.
[tex]\(\frac{5}{2}\)[/tex] can be written as:
[tex]\[
\frac{5}{2} = \frac{5 \times 5}{2 \times 5} = \frac{25}{10}
\][/tex]
Now, we subtract:
[tex]\[
\frac{6}{10} - \frac{25}{10} = \frac{6 - 25}{10} = \frac{-19}{10}
\][/tex]
Converting to decimal form:
[tex]\[
\frac{-19}{10} = -1.9
\][/tex]
3. Divide the Results:
Now, we divide the result of the numerator by the result of the denominator:
[tex]\[
\frac{\frac{-2}{3}}{\frac{-19}{10}} = \frac{-0.6666666666666666}{-1.9}
\][/tex]
This simplifies to:
[tex]\[
\frac{-0.6666666666666666}{-1.9} \approx 0.3508771929824561
\][/tex]
Therefore, the final result of [tex]\(\left[\frac{-8}{9}+\frac{2}{9}\right] \div\left[\frac{6}{10}-\frac{5}{2}\right]\)[/tex] is approximately [tex]\(0.3508771929824561\)[/tex].
