- Simplify the expression by grouping positive terms: \(18 + 5 = 23\).
- Add the negative term to the sum: \(23 + (-11) = 23 - 11 = 12\).
- The final value is \(\boxed{12}\).
Explanation
- Analysis of the expression
The given expression to evaluate is \((-11) + 18 + 5\). This is a simple arithmetic problem involving the addition and subtraction of integers. We can evaluate this expression by either working from left to right or by rearranging the terms, since addition is associative and commutative. Using the property of commutativity, we can group the positive integers together first.
- Calculation steps
To solve \((-11) + 18 + 5\), we can first sum the positive integers:
\[18 + 5 = 23.\]
Now, we substitute this result back into the expression:
\[-11 + 23.\]
Subtracting 11 from 23 gives:
\[23 - 11 = 12.\]
Alternatively, we can evaluate from left to right:
\[-11 + 18 = 7,\]
\[7 + 5 = 12.\]
Both methods yield the same result.
- Final result
The result of the arithmetic expression \((-11) + 18 + 5\) is 12. Therefore, \((-11) + 18 + 5 = \boxed{12}\).
Examples
Arithmetic operations like this are foundational to balancing accounts or tracking changes in quantities. For instance, if you start with a debt of \(\$11\) (represented as \(-11\)), gain \(\$18\), and then gain another \(\$5\), your final balance is \(-11 + 18 + 5 = \$12\). This illustrates how simple additive sequences help track financial gains and losses over time.