Verified Answer :

  • Recognize that subtracting a negative number is equivalent to adding the positive version: \(a - (-b) = a + b\).
  • Apply this rule to the expression \(75 - (-75)\) to rewrite it as \(75 + 75\).
  • Add the two numbers to get the final result: \(150\).
  • The final answer is \(\boxed{150}\).

Explanation

  1. Understanding the Expression

We are given the expression \(75 - (-75)\) and asked to simplify it. This involves understanding the properties of signed numbers and the rules of subtraction. Subtracting a negative number is equivalent to adding the corresponding positive number. Specifically, for any real numbers \(a\) and \(b\), the operation \(a - (-b)\) is identical to \(a + b\).

  1. Applying the Rule of Subtraction

We apply the rule \(a - (-b) = a + b\) to the given expression. Here, \(a = 75\) and \(b = 75\). Substituting these values into the expression, we get:
\[75 - (-75) = 75 + 75\]

  1. Final Calculation

Now, we perform the addition:
\[75 + 75 = 150\]
Thus, the simplified result of the expression \(75 - (-75)\) is \(150\). The final answer is \(\boxed{150}\).

Examples

Understanding how to handle double negatives is essential for managing daily budgets or tracking scores in games. For instance, if you had a credit of \(\$75\) and a debt of \(-\$75\) was removed from your balance, you would effectively add that amount back to your total. Just as \(75 - (-75) = 150\), correctly interpreting these signs ensures that your calculations for resources, points, or finances remain accurate and transparent.

Related Questions