Answer :
To divide fractions, you multiply the first fraction by the reciprocal of the second fraction. Here's how you can solve the given problem step-by-step:
1. Understand the Problem: We need to divide [tex]\(\frac{6}{5}\)[/tex] by [tex]\(-\frac{12}{25}\)[/tex].
2. Find the Reciprocal: The reciprocal of [tex]\(-\frac{12}{25}\)[/tex] is [tex]\(-\frac{25}{12}\)[/tex]. To find the reciprocal, you simply switch the numerator and the denominator, and keep the negative sign.
3. Multiply the Fractions: Multiply [tex]\(\frac{6}{5}\)[/tex] by [tex]\(-\frac{25}{12}\)[/tex]:
[tex]\[
\frac{6}{5} \times -\frac{25}{12} = \frac{6 \times (-25)}{5 \times 12} = \frac{-150}{60}
\][/tex]
4. Simplify the Fraction: Simplify [tex]\(\frac{-150}{60}\)[/tex] by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 30:
[tex]\[
\frac{-150 \div 30}{60 \div 30} = \frac{-5}{2}
\][/tex]
5. Write as a Mixed Number: [tex]\(\frac{-5}{2}\)[/tex] as a mixed number is [tex]\(-2 \frac{1}{2}\)[/tex] or simply [tex]\(-2.5\)[/tex].
So, the solution to [tex]\(\frac{6}{5} \div \left(-\frac{12}{25}\right)\)[/tex] is [tex]\(-2.5\)[/tex].
1. Understand the Problem: We need to divide [tex]\(\frac{6}{5}\)[/tex] by [tex]\(-\frac{12}{25}\)[/tex].
2. Find the Reciprocal: The reciprocal of [tex]\(-\frac{12}{25}\)[/tex] is [tex]\(-\frac{25}{12}\)[/tex]. To find the reciprocal, you simply switch the numerator and the denominator, and keep the negative sign.
3. Multiply the Fractions: Multiply [tex]\(\frac{6}{5}\)[/tex] by [tex]\(-\frac{25}{12}\)[/tex]:
[tex]\[
\frac{6}{5} \times -\frac{25}{12} = \frac{6 \times (-25)}{5 \times 12} = \frac{-150}{60}
\][/tex]
4. Simplify the Fraction: Simplify [tex]\(\frac{-150}{60}\)[/tex] by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 30:
[tex]\[
\frac{-150 \div 30}{60 \div 30} = \frac{-5}{2}
\][/tex]
5. Write as a Mixed Number: [tex]\(\frac{-5}{2}\)[/tex] as a mixed number is [tex]\(-2 \frac{1}{2}\)[/tex] or simply [tex]\(-2.5\)[/tex].
So, the solution to [tex]\(\frac{6}{5} \div \left(-\frac{12}{25}\right)\)[/tex] is [tex]\(-2.5\)[/tex].