Multiply: [tex]\left(-\frac{12}{25}\right)\left(-\frac{10}{16}\right)[/tex].

A. [tex]\frac{3}{10}[/tex]

B. [tex]-\frac{3}{10}[/tex]

C. [tex]-\frac{5}{6}[/tex]

D. [tex]\frac{5}{6}[/tex]

Answer :

To solve the problem of multiplying [tex]\(\left(-\frac{12}{25}\right)\left(-\frac{10}{16}\right)\)[/tex], follow these steps:

1. Understand the Signs: Both fractions are negative, and multiplying two negative numbers will give a positive result.

2. Multiply the Fractions:
- Multiply the numerators: [tex]\(-12\)[/tex] and [tex]\(-10\)[/tex].
- Multiply the denominators: [tex]\(25\)[/tex] and [tex]\(16\)[/tex].

So, the fraction multiplication looks like this:
[tex]\[
\frac{-12 \times -10}{25 \times 16} = \frac{120}{400}
\][/tex]

3. Simplify the Fraction:
- Find the greatest common divisor (GCD) of [tex]\(120\)[/tex] and [tex]\(400\)[/tex]. The GCD is [tex]\(40\)[/tex].
- Divide both the numerator and the denominator by [tex]\(40\)[/tex].

[tex]\[
\frac{120 \div 40}{400 \div 40} = \frac{3}{10}
\][/tex]

4. Final Answer: The simplified result is [tex]\(\frac{3}{10}\)[/tex].

Thus, the product of [tex]\(\left(-\frac{12}{25}\right)\left(-\frac{10}{16}\right)\)[/tex] is [tex]\(\frac{3}{10}\)[/tex].