Simplify using the order of operations.
$\frac{6-(-2)(17)}{-4-2^2}=$
Answer (2)
Evaluate the exponent: 2 2 = 4 .
Evaluate the multiplication: ( − 2 ) ( 17 ) = − 34 .
Simplify the numerator: 6 − ( − 34 ) = 40 .
Simplify the denominator: − 4 − 4 = − 8 .
Divide to get the final answer: − 8 40 = − 5 .
Explanation
Understanding the Problem We are asked to simplify the expression − 4 − 2 2 6 − ( − 2 ) ( 17 ) using the order of operations. The order of operations is Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction (PEMDAS).
Evaluating the Exponent First, we evaluate the exponent in the denominator: 2 2 = 4 . So the expression becomes − 4 − 4 6 − ( − 2 ) ( 17 ) .
Evaluating the Multiplication Next, we evaluate the multiplication in the numerator: ( − 2 ) ( 17 ) = − 34 . So the expression becomes − 4 − 4 6 − ( − 34 ) .
Simplifying the Numerator Now, we simplify the numerator: 6 − ( − 34 ) = 6 + 34 = 40 . So the expression becomes − 4 − 4 40 .
Simplifying the Denominator Then, we simplify the denominator: − 4 − 4 = − 8 . So the expression becomes − 8 40 .
Dividing Numerator by Denominator Finally, we divide the numerator by the denominator: − 8 40 = − 5 .
Final Answer Therefore, the simplified expression is − 5 .
Examples
Understanding the order of operations is crucial in many fields, such as computer programming, engineering, and finance. For example, when writing code, the order in which operations are performed can significantly affect the outcome of a calculation. Similarly, in engineering, calculating stress on a structure requires following the correct order of operations to ensure accurate results. In finance, calculating investment returns or loan payments also relies on the correct application of the order of operations to avoid errors.
The expression − 4 − 2 2 6 − ( − 2 ) ( 17 ) simplifies to − 5 by following the order of operations. We evaluated the exponent, performed multiplication, and then simplified both the numerator and denominator before dividing. The final answer is − 5 .
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