Answer :

To multiply the fractions [tex]\(\frac{12}{25}\)[/tex] and [tex]\(\frac{15}{16}\)[/tex], you follow these steps:

1. Multiply the Numerators:
Multiply the top numbers of the fractions.
[tex]\[
12 \times 15 = 180
\][/tex]

2. Multiply the Denominators:
Multiply the bottom numbers of the fractions.
[tex]\[
25 \times 16 = 400
\][/tex]

3. Form the New Fraction:
Combine the results into a new fraction.
[tex]\[
\frac{180}{400}
\][/tex]

4. Simplify the Fraction:
Simplify [tex]\(\frac{180}{400}\)[/tex] by finding the greatest common divisor (GCD) of 180 and 400, which is 20.

5. Divide Both Numerator and Denominator by their GCD:
[tex]\[
\frac{180 \div 20}{400 \div 20} = \frac{9}{20}
\][/tex]

So, the product of [tex]\(\frac{12}{25}\)[/tex] and [tex]\(\frac{15}{16}\)[/tex] simplifies to [tex]\(\frac{9}{20}\)[/tex].

If you were to convert [tex]\(\frac{9}{20}\)[/tex] into a decimal, it would be [tex]\(0.45\)[/tex]. Therefore, the answer is [tex]\(\frac{9}{20}\)[/tex] or [tex]\(0.45\)[/tex] in decimal form.