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].
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].