Simplify, using the rule for order of operations if necessary:
[tex]5-(5-4)-9=[/tex]
Answer (2)
The expression 5 − ( 5 − 4 ) − 9 simplifies to − 5 by first calculating the value inside the parentheses, replacing it in the expression, and then performing the subtractions sequentially. The order of operations is crucial in arriving at the correct answer. Following these steps ensures clarity in calculation.
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Simplify inside the parentheses: ( 5 − 4 ) = 1 .
Substitute back into the expression: 5 − 1 − 9 .
Perform subtraction from left to right: 5 − 1 = 4 , then 4 − 9 = − 5 .
The simplified expression is − 5 .
Explanation
Understanding the Problem We need to simplify the expression 5 − ( 5 − 4 ) − 9 using the order of operations. The order of operations, often remembered by the acronym PEMDAS, tells us to evaluate expressions in the following order: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
Simplifying Parentheses First, we simplify the expression inside the parentheses: ( 5 − 4 ) = 1 .
Substituting the Result Now, we substitute this result back into the original expression: 5 − 1 − 9 .
Performing Subtraction (Left to Right) Next, we perform the subtraction from left to right: 5 − 1 = 4 , so the expression becomes 4 − 9 .
Final Subtraction Finally, we subtract 9 from 4: 4 − 9 = − 5 . Therefore, the simplified expression is − 5 .
Examples
Understanding order of operations is crucial in many real-life scenarios, such as calculating finances or determining the outcome of a scientific experiment. For instance, if you're calculating the total cost of items with discounts and taxes, following the correct order ensures you get the accurate final amount. Imagine you want to buy a shirt that costs $25, has a discount of $5, and then a tax of 2 i s a ppl i e d . T h ecorrec t c a l c u l a t i o n w o u l d b e (25 - 5) + 2 = 22$, not 25 − ( 5 + 2 ) = 18 , which would be incorrect. This principle applies to more complex calculations in engineering, physics, and economics, where the sequence of operations can significantly impact the result.
