To find the product of [tex]\( 2 \frac{2}{3} \)[/tex] and [tex]\( 3 \frac{3}{8} \)[/tex], we should follow these steps:
1. Convert the mixed numbers to improper fractions:
- For [tex]\( 2 \frac{2}{3} \)[/tex]:
[tex]\[
2 \frac{2}{3} = 2 + \frac{2}{3} = \frac{6}{3} + \frac{2}{3} = \frac{8}{3}
\][/tex]
- For [tex]\( 3 \frac{3}{8} \)[/tex]:
[tex]\[
3 \frac{3}{8} = 3 + \frac{3}{8} = \frac{24}{8} + \frac{3}{8} = \frac{27}{8}
\][/tex]
2. Multiply the improper fractions:
[tex]\[
\frac{8}{3} \times \frac{27}{8}
\][/tex]
3. Simplify the product:
- First, multiply the numerators and the denominators:
[tex]\[
\frac{8 \times 27}{3 \times 8} = \frac{216}{24}
\][/tex]
- Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor which is 24:
[tex]\[
\frac{216 \div 24}{24 \div 24} = \frac{9}{1} = 9
\][/tex]
Thus, the product of [tex]\( 2 \frac{2}{3} \)[/tex] and [tex]\( 3 \frac{3}{8} \)[/tex] is [tex]\(9\)[/tex]. Therefore, the best answer is:
[tex]\[
\boxed{9}
\][/tex]
