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].
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].