To find the product of the fractions [tex]\(\frac{6}{7}\)[/tex] and [tex]\(\frac{3}{13}\)[/tex] and express it in the lowest terms, follow these steps:
1. Multiply the numerators: Multiply the numerators of the fractions together.
[tex]\[
6 \times 3 = 18
\][/tex]
2. Multiply the denominators: Multiply the denominators of the fractions together.
[tex]\[
7 \times 13 = 91
\][/tex]
So the product of the fractions is:
[tex]\[
\frac{6}{7} \cdot \frac{3}{13} = \frac{18}{91}
\][/tex]
3. Simplify the fraction: To simplify the fraction [tex]\(\frac{18}{91}\)[/tex], find the greatest common divisor (GCD) of the numerator and the denominator. For the fraction [tex]\(\frac{18}{91}\)[/tex], the GCD of 18 and 91 is 1.
4. Express in lowest terms: Since the GCD is 1, the fraction [tex]\(\frac{18}{91}\)[/tex] is already in its simplest form.
Thus, the fraction [tex]\(\frac{18}{91}\)[/tex] is the product of [tex]\(\frac{6}{7}\)[/tex] and [tex]\(\frac{3}{13}\)[/tex] and is already in the lowest terms.
The final answer is [tex]\(\frac{18}{91}\)[/tex].
