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 solve the problem of multiplying 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]
The product of the numerators is 120.

2. Multiply the Denominators:
Multiply the denominators of the two fractions:
[tex]\[
25 \times 16 = 400
\][/tex]
The product of the denominators is 400.

3. Create a New Fraction:
The result of multiplying the fractions is:
[tex]\[
\frac{120}{400}
\][/tex]

4. Simplify the Fraction:
First, find the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 120 and 400 is 40.

5. Divide the Numerator and Denominator by the GCD:
Divide both the numerator and the denominator by their GCD to simplify the fraction:
[tex]\[
\frac{120 \div 40}{400 \div 40} = \frac{3}{10}
\][/tex]

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

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