Answer :

To multiply the fractions, we start by multiplying the numerators and denominators separately:

[tex]$$
\frac{12}{25} \cdot \frac{15}{16} = \frac{12 \times 15}{25 \times 16}.
$$[/tex]

Calculating the products:

- Numerator: [tex]$12 \times 15 = 180$[/tex]
- Denominator: [tex]$25 \times 16 = 400$[/tex]

So we have:

[tex]$$
\frac{180}{400}.
$$[/tex]

Next, we simplify the fraction by finding the greatest common divisor (gcd) of [tex]$180$[/tex] and [tex]$400$[/tex]. The gcd of [tex]$180$[/tex] and [tex]$400$[/tex] is [tex]$20$[/tex]. We then divide both the numerator and the denominator by [tex]$20$[/tex]:

[tex]$$
\frac{180 \div 20}{400 \div 20} = \frac{9}{20}.
$$[/tex]

Thus, the simplified result of the multiplication is:

[tex]$$
\frac{9}{20}.
$$[/tex]

Additionally, the decimal equivalent of [tex]$\frac{9}{20}$[/tex] is:

[tex]$$
\frac{9}{20} = 0.45.
$$[/tex]