Verified Answer :

  • Use the commutative property of addition to group \(-24\) and \(24\), which cancel each other out: \(-24 + 24 = 0\).
  • Simplify the remaining terms: \(11 - 3 = 8\).
  • The sum of the simplified terms results in \(\boxed{8}\).

Explanation

  1. Understanding the Problem

The problem requires simplifying the arithmetic expression \(-24 + 11 + 24 - 3\). This involves addition and subtraction of integers. We can utilize the commutative and associative properties of addition, which allow us to rearrange the terms of the expression without changing its value. This makes the calculation more efficient.

  1. Performing the Calculation

We can rearrange the terms to group numbers that are additive inverses of each other or easy to subtract. The expression is \(-24 + 11 + 24 - 3\). We observe that \(-24\) and \(24\) are additive inverses because their sum is \(0\). Therefore, we group them as follows:
\[(-24 + 24) + 11 - 3\]
Now, calculate the sum within the parentheses:
\[0 + 11 - 3\]
This simplifies to:
\[11 - 3\]
Finally, subtracting 3 from 11 gives 8.
\[11 - 3 = 8\]

Examples

In daily life, this simple arithmetic is often used when tracking financial transactions. For example, if you spend \(\$24\) on a book (represented as \(-24\)), receive a \(\$11\) refund (represented as \(+11\)), get another \(\$24\) credit (represented as \(+24\)), and then pay a \(\$3\) service fee (represented as \(-3\)), your net change in balance is \(-24 + 11 + 24 - 3 = 8\). This shows how grouping helps track total gains and losses quickly.

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