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# 1-1 Evaluating Expressions

1-1 Evaluating Expressions. P E M D A S. 1. 2. a. b. c. arentheses. (or other grouping symbols). Within grouping symbols, or if there are no grouping symbols. (in order: left to right ). xponents. }. ultiplication. (in order: left to right ). ivision. }. ddition.

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## 1-1 Evaluating Expressions

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1. 1-1 Evaluating Expressions P E M D A S 1. 2. a. b. c. arentheses (or other grouping symbols) Within grouping symbols, or if there are no grouping symbols. (in order: left to right) xponents } ultiplication (in order: left to right) ivision } ddition (in order: left to right) ubtraction To remember the order think of this phrase: Please Excuse My DearAunt Sally

2. Important definitions & properties. • Algebraic Definition of Subtraction: • For all real #s a and b, a – b = a + -b. • Algebraic Definition of Division: • For all real #s a and b, with b  0, a ÷ b = a  1 . • b • Associative Property of Multiplication: • For any real #s a, b, & c, (ab)c = a(bc) . • Associative Property of Addition: • For any real #s a, b, & c, (a + b) + c = a + (b + c) . • Transitive Property of Equality: • For any real #s a,b, & c, if a = b & b = c, then a = c .

3. 1. Let n = 2. Evaluate a. -4n b. (-4n) 3 3 Problems that ______ to be the _____ are quite ________ with the addition of __________ . appear 3 3 -4 • 2 (-4 • 2) same different -4 • 8 3 (-8) parentheses -512 -32 1-4

4. 1-4 ( ) a + 10 ² b³ + a - 1.5 • Use a calculator to evaluate , • when a = 7 and b = 2. ) ( 7 + 10² 2³ + 7 – 1.5 Step 1: substitute given values for the variables. Step 2: Enter into the calculator using proper notation. (( 7 + 10 ) / (2³ + 7 – 1.5 )) ^ 2 The outer ( ) makes sure that the calculator squares the expression as the last operation performed. The inner ( ) makes sure that the calculator calculates the numerator & denominator before division. Step 3: round the result to the nearest thousandths.  .566649587...  .567

5. Find the volume of a rectangular solid using the • formula V = lwh.Let l = 4 cm, w = 6 cm, & h = 7 cm. V = lwh V = 4  6  7 V = 168 cm³ h w l

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