To determine which mixed number is equivalent to [tex]\(\frac{23}{3}\)[/tex], follow these steps:
1. Divide the numerator by the denominator:
We start by dividing 23 by 3:
[tex]\[
23 \div 3 = 7 \quad \text{with a remainder of} \quad 23 - (3 \times 7) = 23 - 21 = 2.
\][/tex]
2. Express the quotient and the remainder:
The quotient is 7, and the remainder is 2.
3. Write the mixed number:
The mixed number is formed by combining the whole number part (quotient) and the fractional part (remainder over the original denominator). So, it is:
[tex]\[
7 \frac{2}{3}.
\][/tex]
We now need to match this result with the given choices:
- A. [tex]\(7 \frac{1}{3}\)[/tex]
- B. [tex]\(8\)[/tex]
- C. [tex]\(6 \frac{2}{3}\)[/tex]
- D. [tex]\(7 \frac{2}{3}\)[/tex]
From the calculations, we found that [tex]\(\frac{23}{3} \)[/tex] is equivalent to the mixed number [tex]\(7 \frac{2}{3}\)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{D} \][/tex]
