To multiply two fractions, we follow a series of straightforward steps. Here's how the problem [tex]$\frac{9}{4} \cdot \frac{8}{21}$[/tex] can be solved:
1. Multiply the numerators: The numerators of the two fractions are 9 and 8.
[tex]\[
9 \times 8 = 72
\][/tex]
2. Multiply the denominators: The denominators of the two fractions are 4 and 21.
[tex]\[
4 \times 21 = 84
\][/tex]
3. Form the new fraction: Combine the results of the multiplications into a single fraction.
[tex]\[
\frac{72}{84}
\][/tex]
4. Simplify the fraction: To simplify [tex]\(\frac{72}{84}\)[/tex], we need to find the greatest common divisor (GCD) of 72 and 84. The GCD of 72 and 84 is 12.
5. Divide the numerator and the denominator by the GCD:
[tex]\[
\frac{72 \div 12}{84 \div 12} = \frac{6}{7}
\][/tex]
So, the simplified answer for the multiplication of the fractions [tex]\(\frac{9}{4} \cdot \frac{8}{21}\)[/tex] in its lowest terms is:
[tex]\[
\frac{6}{7}
\][/tex]
