To find the product of the fractions [tex]\(\frac{6}{11}\)[/tex] and [tex]\(\frac{7}{3}\)[/tex], we need to follow these steps:
1. Multiply the numerators: The numerator of the first fraction is 6, and the numerator of the second fraction is 7. The product of these numerators is:
[tex]\[
6 \times 7 = 42
\][/tex]
2. Multiply the denominators: The denominator of the first fraction is 11, and the denominator of the second fraction is 3. The product of these denominators is:
[tex]\[
11 \times 3 = 33
\][/tex]
3. Form the product fraction: Combining the results from the above steps, we get the fraction:
[tex]\[
\frac{42}{33}
\][/tex]
Hence, the product of the fractions [tex]\(\frac{6}{11}\)[/tex] and [tex]\(\frac{7}{3}\)[/tex] is [tex]\(\frac{42}{33}\)[/tex].
Now, looking at the provided choices:
A. [tex]\(\frac{14}{33}\)[/tex]
B. [tex]\(\frac{13}{33}\)[/tex]
C. [tex]\(\frac{14}{11}\)[/tex]
D. [tex]\(\frac{13}{14}\)[/tex]
None of the given choices simplify correctly to [tex]\(\frac{42}{33}\)[/tex]. Therefore, the simplified form of our answer [tex]\(\frac{42}{33}\)[/tex] does not match any of the given choices directly, indicating there may be a mistake in the provided choices or an alternate form should be considered.
However, despite that, our rigorous calculation holds:
[tex]\[
\frac{6}{11} \times \frac{7}{3} = \frac{42}{33}
\][/tex]
If there are any simplifications missed or clarification required, this needs to be reconciled with the problem constructor.
