Let's solve the problem step-by-step:
1. Convert Mixed Numbers to Improper Fractions:
- We start with the mixed number [tex]\(-2 \frac{1}{3}\)[/tex]. This can be converted to an improper fraction.
[tex]\[
-2 \frac{1}{3} = -2 - \frac{1}{3} = -\left(2 + \frac{1}{3}\right) = -\left(\frac{6}{3} + \frac{1}{3}\right) = -\frac{7}{3}
\][/tex]
- Next, we have [tex]\(-5\)[/tex]. We can simply consider this as an improper fraction:
[tex]\[
-5 = -\frac{5}{1}
\][/tex]
2. Perform the Subtraction:
- We need to subtract [tex]\(-5\)[/tex] from [tex]\(-2 \frac{1}{3}\)[/tex]:
[tex]\[
-\frac{7}{3} - (-5)
\][/tex]
- Subtracting a negative is equivalent to addition. Hence:
[tex]\[
-\frac{7}{3} + 5
\][/tex]
- To add these fractions, convert [tex]\(5\)[/tex] to a fraction with the same denominator:
[tex]\[
5 = \frac{5 \times 3}{1 \times 3} = \frac{15}{3}
\][/tex]
- Now, add the fractions:
[tex]\[
-\frac{7}{3} + \frac{15}{3} = \frac{-7 + 15}{3} = \frac{8}{3}
\][/tex]
3. Convert the Improper Fraction to a Mixed Number:
- The improper fraction [tex]\(\frac{8}{3}\)[/tex] can be converted to a mixed number.
[tex]\[
8 \div 3 = 2 \text{ remainder } 2
\][/tex]
- This is equivalent to:
[tex]\[
2 \frac{2}{3}
\][/tex]
4. Match the Result with the Given Choices:
- Among the given choices, the correct answer must match [tex]\(2 \frac{2}{3}\)[/tex].
So, the solution to the problem is:
[tex]\[
-2 \frac{1}{3} - (-5) = 2 \frac{2}{3}
\][/tex]
Thus, the correct choice is [tex]\(2 \frac{2}{3}\)[/tex].
