To solve the product of the fractions [tex]\(\frac{3}{12} \times \frac{8}{15}\)[/tex], follow these steps:
1. Multiply the Numerators:
[tex]\[
\text{Numerator} = 3 \times 8 = 24
\][/tex]
2. Multiply the Denominators:
[tex]\[
\text{Denominator} = 12 \times 15 = 180
\][/tex]
So, the resulting fraction is:
[tex]\[
\frac{24}{180}
\][/tex]
3. Simplify the Fraction:
To simplify [tex]\(\frac{24}{180}\)[/tex], find the greatest common divisor (GCD) of 24 and 180. The GCD of 24 and 180 is 12.
Now divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{24 \div 12}{180 \div 12} = \frac{2}{15}
\][/tex]
Thus, the simplified form of the product [tex]\(\frac{3}{12} \times \frac{8}{15}\)[/tex] is:
[tex]\[
\frac{2}{15}
\][/tex]
So the final answer is:
[tex]\(\frac{3}{12} \times \frac{8}{15} = \frac{2}{15}\)[/tex]
