To find the product of [tex]\( 3 \frac{2}{3} \)[/tex] and [tex]\( 14 \frac{2}{5} \)[/tex], we can follow these steps:
1. Convert the mixed fractions to improper fractions:
For [tex]\( 3 \frac{2}{3} \)[/tex]:
[tex]\[
3 \frac{2}{3} = 3 + \frac{2}{3} = \frac{3 \times 3 + 2}{3} = \frac{9 + 2}{3} = \frac{11}{3}
\][/tex]
For [tex]\( 14 \frac{2}{5} \)[/tex]:
[tex]\[
14 \frac{2}{5} = 14 + \frac{2}{5} = \frac{14 \times 5 + 2}{5} = \frac{70 + 2}{5} = \frac{72}{5}
\][/tex]
2. Multiply the improper fractions:
[tex]\[
\frac{11}{3} \times \frac{72}{5} = \frac{11 \times 72}{3 \times 5} = \frac{792}{15}
\][/tex]
3. Simplify the fraction if possible:
The greatest common divisor (GCD) of 792 and 15 is 3. Simplify the fraction [tex]\( \frac{792}{15} \)[/tex]:
[tex]\[
\frac{792 \div 3}{15 \div 3} = \frac{264}{5}
\][/tex]
So, the product of [tex]\( 3 \frac{2}{3} \)[/tex] and [tex]\( 14 \frac{2}{5} \)[/tex] in simplest form is [tex]\( \frac{264}{5} \)[/tex].
4. Find the best match from the choices provided:
The correct answer is:
B. [tex]\(\frac{264}{5}\)[/tex]
