Verified Answer :

  • Apply the property of subtracting a negative number: \(27 - (-19) = 27 + 19\).
  • Add the resulting values: \(27 + 19 = 46\).
  • Complete the expression by performing the final subtraction: \(46 - 5 = 41\).
  • The final result of the expression is \(\boxed{41}\).

Explanation

  1. Analysis of the Expression

We are tasked with finding the value of the numerical expression \(27 - (-19) - 5\). This expression involves both subtraction and the negation of a negative integer. Recall that subtracting a negative number is equivalent to adding the corresponding positive number. That is, the expression \(a - (-b)\) is identical to \(a + b\). Our goal is to simplify this expression systematically.

  1. Simplifying the Subtraction of a Negative Number

First, we address the term \(27 - (-19)\). According to the subtraction rule for negative numbers, we replace the subtraction of a negative value with the addition of its positive counterpart. Thus, we have:
\[27 - (-19) = 27 + 19\]
Performing this addition:
\[27 + 19 = 46\]
Now our expression simplifies to \(46 - 5\).

  1. Calculating the Final Result

Next, we complete the final operation by subtracting \(5\) from the sum obtained in the previous step:
\[46 - 5 = 41\]
Thus, the value of the expression \(27 - (-19) - 5\) is \(41\).

Examples

Understanding how to handle subtractions involving negative numbers is essential in everyday life. For example, if your bank account balance is \(\$27\) and you process a refund (which acts as a negative charge) of \(\$19\), your balance increases to \(\$27 - (-\$19) = \$46\). If you then make a purchase of \(\$5\), your final balance becomes \(\$46 - \$5 = \$41\). Mastering this logic helps you track your finances accurately and understand how various financial transactions affect your total.

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