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1.3 Order of Operations Order of Operations for Evaluating Expressions To evaluate expressions with multiple operations there is an order for evaluation. You may remember it as PEMDAS: parentheses, exponents, multiplication and division, addition and subtraction. Example Evaluate 2 + 3(1 + 4). 2 + 3(1 + 4) = 2 + 3(5) = 2 + 15 = 17 Example Evaluate 8 − [(4 − 7) + (8 − 1)]. 8 − [(4 − 7) + (8 − 1)] = 8 − (−3 + 7) =8−4 =4 Consider (−2)2 vs −22 . (−2)2 = (−2)(−2) = 4 whereas −22 = −(2 · 2) = −4. In the second one, without parentheses, the exponent is only applied to the 2. The negative is considered multiplication by −1 and so exponents first. Consider 5+2 . The fraction bar presents the grouping and so parentheses are not necessary. 1+4·5 5+2 1+4·5 = 7 1 + 20 = 7 21 = 1 3 If I were to enter this into my calculator as one expression, I would enter the following: (5 + 2) ÷ (1 + 4 · 5)