Simplify: $-(8-10)-(3-11)=$
Answer (2)
To simplify the expression − ( 8 − 10 ) − ( 3 − 11 ) , first evaluate the expressions in the parentheses to get − 2 and − 8 . Substitute these values to get 2 + 8 , which simplifies to 10 . Therefore, the final answer is oxed{10} .
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Evaluate the expression inside the first parentheses: 8 − 10 = − 2 .
Evaluate the expression inside the second parentheses: 3 − 11 = − 8 .
Substitute the values back into the original expression: − ( − 2 ) − ( − 8 ) .
Simplify the expression: 2 + 8 = 10 .
The final answer is 10 .
Explanation
Understanding the problem We need to evaluate the expression − ( 8 − 10 ) − ( 3 − 11 ) using the order of operations. The order of operations tells us to evaluate expressions inside parentheses first.
Evaluating the first parentheses First, we evaluate the expression inside the first parentheses: 8 − 10 = − 2 .
Evaluating the second parentheses Next, we evaluate the expression inside the second parentheses: 3 − 11 = − 8 .
Substituting the values Now we substitute these values back into the original expression: − ( − 2 ) − ( − 8 ) .
Simplifying the expression A negative times a negative is a positive, so we have 2 − ( − 8 ) .
Further simplification Subtracting a negative is the same as adding a positive, so we have 2 + 8 .
Final calculation Finally, we add the numbers: 2 + 8 = 10 .
Examples
Understanding order of operations is crucial in many real-life scenarios, such as calculating financial transactions or determining the outcome of a scientific experiment. For example, if you are calculating the total cost of items with discounts and taxes, you need to follow the correct order to get the accurate final price. Similarly, in programming, the order of operations determines how expressions are evaluated, which can affect the program's output. Mastering this concept ensures accurate and reliable results in various fields.
