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Chapter 1: Sets, Operations and Algebraic Language TEACHER 1.7: Order of Operations The PEMDAS Pyramid (Please excuse my dear aunt Sally’s Labrador Retriever.”) P E M A D S (LEFT TO RIGHT) Level 1 P Perform any operations inside grouping symbols such as parenthesis, brackets, and absolute value signs. When a fraction bar is involved, add parentheses around the numerator and around the denominator. Level 2 E Level 3 M&D Simplify any terms with exponents. Level 4 A&S Perform any operations involving addition and subtraction. In levels 3 and 4, if there are two or more operations on the same level of the pyramid, start with the operation that is furthest left and proceed to the right. Perform any operations involving multiplication and division. Sample Problem The expression 15 – 3[2 + 6(–3)] simplifies to (1) –45 (3) 63 (2) –33 (4) 192 The first step is the inner-most parenthesis 15 - 3[2 + 6(-3)] 15 - 3[2 + (-18)] The next step is still in the inner parentheses 15 - 3[2 + (-18)] 15 - 3[-16] Now we have a choice between multiplication and subtraction. Multiplication comes first. 15 - 3[-16] 15 +48 Now all we have left is the addition: 15+48=63 1 Chapter 1: Sets, Operations and Algebraic Language TEACHER 1.7: Order of Operations Correct Order of Operations Correct Incorrect Order of Operations Wrong 6 × (5 + 3) = 6 × 8 = 48 6 × (5 + 3) = 30 + 3 = 33 (wrong) 2 + 5 × 3 = 2 + 15 = 17 2 + 5 × 3 = 7 × 3 = 21 (wrong) 5 × 22 = 5 × 4 = 20 5 × 22 = 102 = 100 (wrong) 30 ÷ 5 × 3 = 6 × 3 = 18 30 ÷ 5 × 3 = 30 ÷ 15 = 2 REGENTS QUESTIONS 1 (wrong) SOLUTIONS (3) 6 is Using the acronym PEMDASLR 2 indicates that addition and subtraction evaluated, what would be done last? operations should be performed from (1) subtracting (3) adding left to right. Since the addition is to the (2) squaring (4) dividing right of the subtraction, the addition would be done last. If the expression 3 42 (4) 2 What is the first step in simplifying the expression (2 3 4 5) 2 ? (1) square 5 (2) add 4 and 5 (3) subtract 3 from 2 (4) multiply 3 by 4 3 The expression 15 – 3[2 + 6(–3)] simplifies to (1) –45 (3) 63 (2) –33 (4) 192 15 – 3[2 + 6(–3)] 15 – 3[2 + (-18)] 15 – 3[-16] 15 + 48 63 4 On February 18, from 9 a.m. until 2 p.m., the temperature rose from –14°F (1) 36 – (-14) = 50 2 Using the acronym PEMDASLR indicates that operations inside the expression’s parentheses should be performed first. Multiplication precedes addition. (3) Chapter 1: Sets, Operations and Algebraic Language TEACHER 1.7: Order of Operations to 36°F. What was the total increase in Perhaps the easiest Regents question ever, temperature during this time period? requiring only the subtraction of two (1) 50° (3) 32° integers. (2) 36° (4) 22° 3