What is the quotient of $-\frac{3}{8}$ and $-\frac{1}{3}$?
To compute the quotient of \(-\frac{3}{8}\) and \(-\frac{1}{3}\), we denote the operation as:
\[ \frac{-\frac{3}{8}}{-\frac{1}{3}} \]
Recall that dividing by a fraction is equivalent to multiplying by its reciprocal. The reciprocal of \(-\frac{1}{3}\) is \(-\frac{3}{1} = -3\).
Thus, the division becomes:
\[ \left(-\frac{3}{8}\right) \times \left(-\frac{3}{1}\right) \]
Since the product of two negative numbers is positive, we have:
\[ \left(-\frac{3}{8}\right) \times (-3) = \frac{3 \times 3}{8 \times 1} = \frac{9}{8} \]
Converting the improper fraction \(\frac{9}{8}\) into a mixed number, we divide 9 by 8 to get 1 with a remainder of 1. Therefore:
\[ \frac{9}{8} = 1 \frac{1}{8} \]
Comparing this result to the provided option, \(-1 \frac{1}{8}\), we see that the given option is incorrect because the correct quotient is \(1 \frac{1}{8}\).
In a real-life scenario, you might be dividing a total debt of \(\$ \frac{3}{8}\) million by a specific factor of \(-\frac{1}{3}\) to determine a quarterly adjustment in a financial model. Understanding how signs and reciprocals behave when dividing fractions ensures that you accurately track balances and budget changes. This is a fundamental skill in arithmetic that helps prevent errors in financial or data-driven planning.