Answer :

To solve the multiplication of the fractions [tex]\(\frac{12}{25} \cdot \frac{15}{16}\)[/tex], follow these steps:

1. Multiply the Numerators:
- Take the numerator of the first fraction (12) and multiply it by the numerator of the second fraction (15):
[tex]\[
12 \times 15 = 180
\][/tex]

2. Multiply the Denominators:
- Take the denominator of the first fraction (25) and multiply it by the denominator of the second fraction (16):
[tex]\[
25 \times 16 = 400
\][/tex]

3. Form the New Fraction:
- The result is a new fraction with the numerator from step 1 and the denominator from step 2:
[tex]\[
\frac{180}{400}
\][/tex]

4. Simplify the Fraction:
- Find the greatest common divisor (GCD) of 180 and 400 to simplify the fraction. The GCD of 180 and 400 is 20.
- Divide the numerator and the denominator by their GCD:
[tex]\[
\frac{180 \div 20}{400 \div 20} = \frac{9}{20}
\][/tex]

5. Convert to Decimal:
- Lastly, to express the result as a decimal, divide the numerator by the denominator:
[tex]\[
\frac{9}{20} = 0.45
\][/tex]

Therefore, [tex]\(\frac{12}{25} \cdot \frac{15}{16} = 0.45\)[/tex], or in simplest fraction form, [tex]\(\frac{9}{20}\)[/tex].