Answer :
To solve the problem [tex]\(\frac{16}{5} \div \left(-\frac{12}{25}\right)\)[/tex], we can follow these steps:
1. Reciprocal of the Second Fraction: When dividing by a fraction, you multiply by its reciprocal. The reciprocal of [tex]\(-\frac{12}{25}\)[/tex] is [tex]\(-\frac{25}{12}\)[/tex].
2. Multiply the Fractions: Multiply [tex]\(\frac{16}{5}\)[/tex] by [tex]\(-\frac{25}{12}\)[/tex].
[tex]\[
\frac{16}{5} \times \left(-\frac{25}{12}\right) = \frac{16 \times (-25)}{5 \times 12} = \frac{-400}{60}
\][/tex]
3. Simplify the Fraction: Now, simplify [tex]\(\frac{-400}{60}\)[/tex].
- Find the greatest common divisor (GCD) of 400 and 60, which is 20.
- Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{-400 \div 20}{60 \div 20} = \frac{-20}{3}
\][/tex]
So, the answer in simplest form is [tex]\(-\frac{20}{3}\)[/tex], which is a negative fraction. If you prefer to write it as a mixed number, it would be [tex]\(-6 \frac{2}{3}\)[/tex].
1. Reciprocal of the Second Fraction: When dividing by a fraction, you multiply by its reciprocal. The reciprocal of [tex]\(-\frac{12}{25}\)[/tex] is [tex]\(-\frac{25}{12}\)[/tex].
2. Multiply the Fractions: Multiply [tex]\(\frac{16}{5}\)[/tex] by [tex]\(-\frac{25}{12}\)[/tex].
[tex]\[
\frac{16}{5} \times \left(-\frac{25}{12}\right) = \frac{16 \times (-25)}{5 \times 12} = \frac{-400}{60}
\][/tex]
3. Simplify the Fraction: Now, simplify [tex]\(\frac{-400}{60}\)[/tex].
- Find the greatest common divisor (GCD) of 400 and 60, which is 20.
- Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{-400 \div 20}{60 \div 20} = \frac{-20}{3}
\][/tex]
So, the answer in simplest form is [tex]\(-\frac{20}{3}\)[/tex], which is a negative fraction. If you prefer to write it as a mixed number, it would be [tex]\(-6 \frac{2}{3}\)[/tex].