To multiply the fractions [tex]\(\frac{4}{11}\)[/tex] and [tex]\(\frac{10}{8}\)[/tex], follow these steps:
1. Multiply the numerators (the top parts of the fractions):
[tex]\[
4 \times 10 = 40
\][/tex]
2. Multiply the denominators (the bottom parts of the fractions):
[tex]\[
11 \times 8 = 88
\][/tex]
3. Combine the results to form a new fraction:
[tex]\[
\frac{40}{88}
\][/tex]
4. Simplify the fraction by finding the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 40 and 88 is 8.
5. Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{40 \div 8}{88 \div 8} = \frac{5}{11}
\][/tex]
So, the product of [tex]\(\frac{4}{11}\)[/tex] and [tex]\(\frac{10}{8}\)[/tex] in its simplest form is:
[tex]\[
\boxed{\frac{5}{11}}
\][/tex]
