To find the quotient \(-12 \div \frac{20}{12}\), we can use the property of division that states dividing by a fraction is the same as multiplying by its reciprocal.
First, we take the reciprocal of \(\frac{20}{12}\), which is \(\frac{12}{20}\).
Now, we rewrite the expression:
\[ -12 \div \frac{20}{12} = -12 \times \frac{12}{20} \]
Next, we perform the multiplication:
\[ -12 \times \frac{12}{20} = \frac{-12 \times 12}{20} = \frac{-144}{20} \]
Now, simplify \(\frac{-144}{20}\). To do this, we can find the greatest common divisor (GCD) of 144 and 20, which is 4.
Now, divide both the numerator and the denominator by their GCD:
\[ \frac{-144 \div 4}{20 \div 4} = \frac{-36}{5} \]
Thus, the final result is:
\[ -36/5 \]
Looking at the answer choices provided:
A. \(-\frac{7}{80}\)
B. \(-\frac{5}{63}\)
C. \(-\frac{80}{7}\)
D. \(-\frac{63}{5}\)
None of the provided options is \(-\frac{36}{5}\). It appears that there might be a mistake in the options or in the interpretation of the problem. Based strictly on the calculation, the result is \(-\frac{36}{5}\), which is not listed among your choices.