Verified Answer :

  • Rewrite the expression \(27 - (-19) - 5\) by converting the double negative into an addition: \(27 + 19 - 5\).
  • Perform the addition: \(27 + 19 = 46\).
  • Perform the subtraction: \(46 - 5 = 41\).
  • The final value of the expression is \(\boxed{41}\).

Explanation

  1. Problem Analysis

The objective is to calculate the value of the arithmetic expression \(27 - (-19) - 5\). We start by analyzing the components of the expression. It contains three terms combined by subtraction and addition (since subtracting a negative number is equivalent to adding its absolute value). We will apply the standard order of operations to evaluate the expression systematically.

  1. Rewriting the Expression

The first step is to handle the double negative sign. In mathematics, subtracting a negative number is equivalent to adding its positive counterpart. Therefore, we can rewrite \(-(-19)\) as \(+19\). The expression then becomes:
\[27 + 19 - 5\]

  1. Calculation and Final Result

Now, we perform the operations from left to right.
First, add \(27\) and \(19\):
\[27 + 19 = 46\]
Next, subtract \(5\) from the result:
\[46 - 5 = 41\]
Thus, the value of the expression is \(41\).

Examples

Calculating expressions with negative numbers is essential in everyday life, such as when tracking your bank account balance. For example, if you start with a balance of \$27, owe a debt of \$19 (represented as -(-19) when the debt is forgiven), and then spend \$5, your final balance is \(27 - (-19) - 5 = 41\). Mastering these operations helps in managing finances, budgeting, and solving various real-world quantitative problems.

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