Find the quotient:
$\frac{42}{-3}$
The problem asks us to evaluate the quotient of the division expression \(\frac{42}{-3}\). We have a positive integer, 42, being divided by a negative integer, -3. The division of two numbers with opposite signs results in a negative value. Therefore, we expect the result of our calculation to be negative.
To compute the final quotient, we can divide the absolute values of the numerator and the denominator and then apply a negative sign to the result. The absolute value of the numerator is \(|42| = 42\), and the absolute value of the denominator is \(|-3| = 3\). Performing the division of these absolute values, we have \(\frac{42}{3} = 14\). Since the signs of the original numbers were different, the final result is \(-14\).
In real life, division with signed numbers often appears in contexts involving debt, temperature changes, or coordinate systems. For instance, if a company reports a total debt (a negative value) of \(\$42\) to be split equally among 3 departments, each department would be responsible for \(\frac{-42}{3} = -\$14\) of the debt. Similarly, if a submarine descends 42 meters in 3 minutes at a constant rate, its vertical position relative to the starting point changes at a rate of \(\frac{-42}{3} = -14\) meters per minute. These operations help us track changes in quantities where direction or state matters.