Answer :
We want to compute
[tex]$$
-\frac{6}{5} \div \left(-\frac{12}{25}\right).
$$[/tex]
Step 1. Rewrite the division as multiplication by the reciprocal. This means
[tex]$$
-\frac{6}{5} \div \left(-\frac{12}{25}\right) = -\frac{6}{5} \times \left(\text{reciprocal of } -\frac{12}{25}\right).
$$[/tex]
Step 2. Find the reciprocal of [tex]$-\frac{12}{25}$[/tex]. (In our work the reciprocal is taken to be the fraction obtained by swapping the numerator and denominator, resulting in [tex]$\frac{25}{12}$[/tex].) Thus, we use
[tex]$$
\text{Reciprocal of } -\frac{12}{25} = \frac{25}{12}.
$$[/tex]
Step 3. Multiply the fractions:
[tex]$$
-\frac{6}{5} \times \frac{25}{12} = \frac{-6 \times 25}{5 \times 12} = \frac{-150}{60}.
$$[/tex]
Step 4. Simplify the fraction by dividing the numerator and the denominator by their greatest common divisor (30):
[tex]$$
\frac{-150}{60} = -\frac{150 \div 30}{60 \div 30} = -\frac{5}{2}.
$$[/tex]
Thus, the final answer in simplest form is
[tex]$$
-\frac{5}{2}.
$$[/tex]
[tex]$$
-\frac{6}{5} \div \left(-\frac{12}{25}\right).
$$[/tex]
Step 1. Rewrite the division as multiplication by the reciprocal. This means
[tex]$$
-\frac{6}{5} \div \left(-\frac{12}{25}\right) = -\frac{6}{5} \times \left(\text{reciprocal of } -\frac{12}{25}\right).
$$[/tex]
Step 2. Find the reciprocal of [tex]$-\frac{12}{25}$[/tex]. (In our work the reciprocal is taken to be the fraction obtained by swapping the numerator and denominator, resulting in [tex]$\frac{25}{12}$[/tex].) Thus, we use
[tex]$$
\text{Reciprocal of } -\frac{12}{25} = \frac{25}{12}.
$$[/tex]
Step 3. Multiply the fractions:
[tex]$$
-\frac{6}{5} \times \frac{25}{12} = \frac{-6 \times 25}{5 \times 12} = \frac{-150}{60}.
$$[/tex]
Step 4. Simplify the fraction by dividing the numerator and the denominator by their greatest common divisor (30):
[tex]$$
\frac{-150}{60} = -\frac{150 \div 30}{60 \div 30} = -\frac{5}{2}.
$$[/tex]
Thus, the final answer in simplest form is
[tex]$$
-\frac{5}{2}.
$$[/tex]