Answer :
To solve the division of two fractions [tex]\(-\frac{8}{5} \div \frac{12}{25}\)[/tex], we can follow these steps:
1. Understand Division of Fractions: Dividing by a fraction is the same as multiplying by its reciprocal. So, we'll multiply [tex]\(-\frac{8}{5}\)[/tex] by the reciprocal of [tex]\(\frac{12}{25}\)[/tex].
2. Find the Reciprocal: The reciprocal of [tex]\(\frac{12}{25}\)[/tex] is [tex]\(\frac{25}{12}\)[/tex].
3. Multiply the Fractions: Now, multiply [tex]\(-\frac{8}{5}\)[/tex] by [tex]\(\frac{25}{12}\)[/tex].
[tex]\[
-\frac{8}{5} \times \frac{25}{12}
\][/tex]
4. Multiply the Numerators: Calculate the product of the numerators:
[tex]\[
-8 \times 25 = -200
\][/tex]
5. Multiply the Denominators: Calculate the product of the denominators:
[tex]\[
5 \times 12 = 60
\][/tex]
6. Create a New Fraction: Combine the results:
[tex]\[
\frac{-200}{60}
\][/tex]
7. Simplify the Fraction: To simplify [tex]\(\frac{-200}{60}\)[/tex], we need to find the greatest common divisor (GCD) of 200 and 60, which is 20. Divide both the numerator and the denominator by 20.
[tex]\[
\frac{-200 \div 20}{60 \div 20} = \frac{-10}{3}
\][/tex]
So, the answer to [tex]\(-\frac{8}{5} \div \frac{12}{25}\)[/tex] is [tex]\(-\frac{10}{3}\)[/tex], which is a simplified improper fraction. If you want to convert it to a mixed number, it would be [tex]\(-3\frac{1}{3}\)[/tex].
1. Understand Division of Fractions: Dividing by a fraction is the same as multiplying by its reciprocal. So, we'll multiply [tex]\(-\frac{8}{5}\)[/tex] by the reciprocal of [tex]\(\frac{12}{25}\)[/tex].
2. Find the Reciprocal: The reciprocal of [tex]\(\frac{12}{25}\)[/tex] is [tex]\(\frac{25}{12}\)[/tex].
3. Multiply the Fractions: Now, multiply [tex]\(-\frac{8}{5}\)[/tex] by [tex]\(\frac{25}{12}\)[/tex].
[tex]\[
-\frac{8}{5} \times \frac{25}{12}
\][/tex]
4. Multiply the Numerators: Calculate the product of the numerators:
[tex]\[
-8 \times 25 = -200
\][/tex]
5. Multiply the Denominators: Calculate the product of the denominators:
[tex]\[
5 \times 12 = 60
\][/tex]
6. Create a New Fraction: Combine the results:
[tex]\[
\frac{-200}{60}
\][/tex]
7. Simplify the Fraction: To simplify [tex]\(\frac{-200}{60}\)[/tex], we need to find the greatest common divisor (GCD) of 200 and 60, which is 20. Divide both the numerator and the denominator by 20.
[tex]\[
\frac{-200 \div 20}{60 \div 20} = \frac{-10}{3}
\][/tex]
So, the answer to [tex]\(-\frac{8}{5} \div \frac{12}{25}\)[/tex] is [tex]\(-\frac{10}{3}\)[/tex], which is a simplified improper fraction. If you want to convert it to a mixed number, it would be [tex]\(-3\frac{1}{3}\)[/tex].