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], we'll follow these steps:

1. Understand the sign change: When multiplying two negative numbers, the result is positive. So the product of [tex]\(-\frac{12}{25}\)[/tex] and [tex]\(-\frac{10}{16}\)[/tex] will be positive.

2. Multiply the numerators:
[tex]\[
12 \times 10 = 120
\][/tex]

3. Multiply the denominators:
[tex]\[
25 \times 16 = 400
\][/tex]

4. Form the fraction:
[tex]\[
\frac{120}{400}
\][/tex]

5. Simplify the fraction: To simplify [tex]\(\frac{120}{400}\)[/tex], we find the greatest common divisor (GCD) of the numerator and denominator, which is 40. Divide both by 40:

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

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

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