To multiply the fractions [tex]\(\frac{11}{6}\)[/tex] and [tex]\(\frac{5}{7}\)[/tex], follow these steps:
1. Multiply the numerators: The numerators are the top numbers of the fractions.
[tex]\[
11 \times 5 = 55
\][/tex]
2. Multiply the denominators: The denominators are the bottom numbers of the fractions.
[tex]\[
6 \times 7 = 42
\][/tex]
Now the product of the fractions is [tex]\(\frac{55}{42}\)[/tex].
3. Simplify the fraction (if possible): To do this, find the greatest common divisor (GCD) of the numerator and the denominator and divide both by this number.
In this case, the GCD of 55 and 42 is 1 (they have no other common divisors except 1). Therefore, [tex]\(\frac{55}{42}\)[/tex] is already in its simplest form.
So the product of [tex]\(\frac{11}{6}\)[/tex] and [tex]\(\frac{5}{7}\)[/tex] is [tex]\(\frac{55}{42}\)[/tex].
Final answer:
[tex]\[
\frac{11}{6} \times \frac{5}{7} = \frac{55}{42}
\][/tex]
