Answer :

Sure! Let's solve the problem step-by-step.

We are given the fractions [tex]\(\frac{12}{25}\)[/tex] and [tex]\(\frac{15}{18}\)[/tex] to multiply. Here's the detailed process to find the product of these two fractions:

1. Multiply the numerators (top numbers) together:
[tex]\[
12 \times 15 = 180
\][/tex]

2. Multiply the denominators (bottom numbers) together:
[tex]\[
25 \times 18 = 450
\][/tex]

3. Form the new fraction using the products from steps 1 and 2:
[tex]\[
\frac{180}{450}
\][/tex]

4. Simplify the fraction by finding the greatest common divisor (GCD) of the numerator and the denominator:
- The GCD of 180 and 450 is 90.
- To simplify, divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{180 \div 90}{450 \div 90} = \frac{2}{5}
\][/tex]

So, the simplified result of [tex]\(\frac{12}{25} \cdot \frac{15}{18}\)[/tex] is [tex]\(\frac{2}{5}\)[/tex], which is equivalent to 0.4 as a decimal.

Thus, [tex]\(\frac{12}{25} \cdot \frac{15}{18} = 0.4\)[/tex].