To find the absolute value of the expression [tex]\(\left|-\frac{2}{3}-\frac{5}{3}\right|\)[/tex], let's go through the steps systematically:
1. Simplify the Expression Inside the Absolute Value:
- Start with the expression inside the absolute value: [tex]\(-\frac{2}{3} - \frac{5}{3}\)[/tex].
- Both fractions have a common denominator (3), so we can combine them:
[tex]\[
-\frac{2}{3} - \frac{5}{3} = -\left(\frac{2}{3} + \frac{5}{3}\right)
\][/tex]
- Adding the numerators:
[tex]\[
\frac{2}{3} + \frac{5}{3} = \frac{2+5}{3} = \frac{7}{3}
\][/tex]
- Therefore, the expression simplifies to:
[tex]\[
-\frac{7}{3}
\][/tex]
2. Find the Absolute Value:
- The absolute value of a number is its distance from zero on the number line, regardless of direction (always a non-negative value).
- So, we need the absolute value of [tex]\(-\frac{7}{3}\)[/tex]:
[tex]\[
\left|-\frac{7}{3}\right| = \frac{7}{3}
\][/tex]
3. Convert to Decimal Form for Clarity:
- Convert [tex]\(\frac{7}{3}\)[/tex] to a decimal:
[tex]\[
\frac{7}{3} \approx 2.3333333333333335
\][/tex]
Hence, the absolute value of the given expression [tex]\(\left|-\frac{2}{3}-\frac{5}{3}\right|\)[/tex] is approximately 2.3333333333333335.
