To find the quotient of the division [tex]\(\frac{8}{3} \div \frac{2}{3}\)[/tex], we can follow these steps:
1. Understand the division of fractions: When dividing fractions, you multiply by the reciprocal of the divisor. In other words:
[tex]\[
\frac{8}{3} \div \frac{2}{3} = \frac{8}{3} \times \frac{3}{2}
\][/tex]
2. Multiply the numerators and the denominators:
[tex]\[
\frac{8 \times 3}{3 \times 2} = \frac{24}{6}
\][/tex]
3. Simplify the fraction:
[tex]\[
\frac{24}{6} = 4
\][/tex]
Therefore, the quotient in its simplest form is [tex]\(4\)[/tex].
So, the correct answer is:
D. 4
