To solve the multiplication of the fractions [tex]\(\frac{6}{20} \cdot \frac{4}{15}\)[/tex], follow these steps:
1. Multiply the numerators:
The numerators of the fractions are 6 and 4.
[tex]\[
6 \times 4 = 24
\][/tex]
2. Multiply the denominators:
The denominators of the fractions are 20 and 15.
[tex]\[
20 \times 15 = 300
\][/tex]
So, the product of the fractions before simplifying is:
[tex]\[
\frac{24}{300}
\][/tex]
3. Simplify the fraction:
To simplify the fraction [tex]\(\frac{24}{300}\)[/tex], we need to find the greatest common divisor (GCD) of 24 and 300.
The GCD of 24 and 300 is 12.
Now, divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{24 \div 12}{300 \div 12} = \frac{2}{25}
\][/tex]
Therefore, the simplified form of the product is:
[tex]\[
\frac{6}{20} \cdot \frac{4}{15} = \frac{2}{25}
\][/tex]
