Verified Answer :

  • Recognize that adding two negative integers involves adding their absolute values and keeping the negative sign.
  • Express the sum as \(-(70 + 31)\).
  • Perform the arithmetic calculation \(70 + 31 = 101\).
  • Apply the negative sign to obtain the final result: \(\boxed{-101}\).

Explanation

  1. Understanding the Addition of Negative Integers

We are tasked to find the sum of two negative integers, -70 and -31. This can be represented by the expression \(-70 + (-31)\). When adding two numbers with the same sign, we add their absolute values and maintain the common sign. In this case, both numbers are negative, so we will sum their magnitudes and make the final result negative.

  1. Performing the Calculation

To calculate \(-70 + (-31)\), we can factor out the negative sign:
\[-70 + (-31) = -(70 + 31)\]
Next, we perform the addition inside the parentheses:
\[70 + 31 = 101\]
Finally, we apply the negative sign to the result:
\[-(101) = -101\]
Thus, \(-70 + (-31) = -101\).

Examples

Adding negative numbers is frequently used in financial scenarios. For instance, if you withdraw \(\$70\) from your bank account and then make an additional withdrawal of \(\$31\), your account balance changes by \(-70 + (-31) = -101\). This represents a total decrease of \(\$101\) in your balance. Understanding these operations helps in managing budgets and calculating debt accumulation.

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