Answer :

To solve the problem [tex]\(\frac{12}{25} \times \frac{5}{6}\)[/tex] and simplify the result, follow these steps:

1. Multiply the Numerators:
- Take the numerators of both fractions: 12 and 5.
- Multiply them together: [tex]\(12 \times 5 = 60\)[/tex].

2. Multiply the Denominators:
- Take the denominators of both fractions: 25 and 6.
- Multiply them together: [tex]\(25 \times 6 = 150\)[/tex].

3. Form the New Fraction:
- The result of the multiplication is [tex]\(\frac{60}{150}\)[/tex].

4. Simplify the Fraction:
- To simplify [tex]\(\frac{60}{150}\)[/tex], find the greatest common divisor (GCD) of 60 and 150. This GCD is 30.
- Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{60 \div 30}{150 \div 30} = \frac{2}{5}
\][/tex]

So, [tex]\(\frac{12}{25} \times \frac{5}{6}\)[/tex] simplifies to [tex]\(\frac{2}{5}\)[/tex].