High School

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

A. [tex]\frac{5}{6}[/tex]
B. [tex]\frac{3}{10}[/tex]
C. [tex]-\frac{3}{10}[/tex]
D. [tex]-\frac{5}{6}[/tex]

Answer :

To multiply the fractions [tex]\(-\frac{12}{25}\)[/tex] and [tex]\(-\frac{10}{16}\)[/tex], follow these steps:

1. Multiply the Numerators:

Multiply the numerators of the two fractions:
[tex]\[
-12 \times -10 = 120
\][/tex]

2. Multiply the Denominators:

Multiply the denominators of the two fractions:
[tex]\[
25 \times 16 = 400
\][/tex]

3. Form the Fraction:

Now that you have the product of the numerators and the denominators, form the new fraction:
[tex]\[
\frac{120}{400}
\][/tex]

4. Simplify the Fraction:

To simplify [tex]\(\frac{120}{400}\)[/tex], find the greatest common divisor (GCD) of 120 and 400, which is 40. Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{120 \div 40}{400 \div 40} = \frac{3}{10}
\][/tex]

The simplified product of the fractions [tex]\(-\frac{12}{25}\)[/tex] and [tex]\(-\frac{10}{16}\)[/tex] is [tex]\(\frac{3}{10}\)[/tex].

Thus, the correct answer is [tex]\(\frac{3}{10}\)[/tex].