Verified Answer :

  • Identify the expression \(-87 - (-66)\).
  • Recognize that subtracting a negative number is equivalent to adding its positive value: \(-87 + 66\).
  • Calculate the difference between the absolute values: \(87 - 66 = 21\).
  • Apply the negative sign to the result because the original negative number had a larger absolute value: \(\boxed{-21}\).

Explanation

  1. Problem Analysis

The problem requires evaluating the expression \(-87 - (-66)\). In arithmetic, subtracting a negative number is equivalent to adding its positive counterpart. The rule is expressed as \(-a - (-b) = -a + b\). Our goal is to simplify this expression to find the final numerical value.

  1. Applying Subtraction Rules

Using the rule for subtraction of signed numbers, we rewrite the expression \(-87 - (-66)\) as follows:
\[-87 - (-66) = -87 + 66\]
This transformation turns the subtraction of a negative number into the addition of a positive number. Now, the task is to add 66 to -87.

  1. Performing the Calculation

To add \(66\) to \(-87\), we look at the difference between their absolute values because they have opposite signs. The absolute values are \(|-87| = 87\) and \(|66| = 66\). We subtract the smaller absolute value from the larger one:
\[87 - 66 = 21\]
Since the number with the larger absolute value, \(-87\), is negative, the final result will carry the negative sign:
\[-87 + 66 = -21\]
Thus, the simplified result of the expression \(-87 - (-66)\) is \(-21\).

Examples

Understanding the subtraction of negative numbers is essential in real-life contexts like finance or meteorology. For instance, if your bank account has a balance of \(-87\) dollars (meaning you owe the bank 87 dollars) and you receive a credit of 66 dollars, your new balance is calculated as \(-87 + 66 = -21\) dollars. This helps in tracking debt and managing assets effectively.

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