What is the value of $(-127)-62-(-15)$?
The objective is to evaluate the numerical expression \((-127) - 62 - (-15)\). We identify this as a series of integer subtractions. Recall that subtracting a number is equivalent to adding its additive inverse (or opposite). Specifically, the subtraction of a negative number, \(a - (-b)\), is equivalent to addition, \(a + b\). The expression involves three terms: \(-127\), \(-62\), and \(+15\).
To solve the expression \((-127) - 62 - (-15)\), we first handle the subtractions systematically. We can rewrite the expression by changing the subtractions into additions of opposites:
\((-127) - 62 = -189\)
Next, we add the final term, which is the additive inverse of \(-15\), effectively adding \(15\):
\(-189 + 15 = -174\)
Thus, the value of the expression is \(-174\). Comparing this result with the provided options (\(-174, -50, -204, -80\)), we see that \(-174\) is the correct choice.
In real life, this type of calculation often represents tracking a balance. For instance, if a bank account starts with a debt of \(\$127\) (represented as \(-127\)), then you withdraw another \(\$62\) (represented by subtracting \(\$62\)), and finally receive a refund of \(\$15\) (represented by subtracting \(-15\)), the final balance is \((-127) - 62 + 15 = -174\). This calculation helps manage finances and understand how debits and credits affect a total.