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§4.3 Order of Operations 02/16/17 Today We’ll Discuss How do we evaluate algebraic expressions? How do we use the order of operations? Numerical Expression Definition: A collection of numbers and operation symbols is a numerical expression. Algebraic Expression Definition: A collection of variables, numbers, and operation symbols is an algebraic expression. To evaluate an algebraic expression is to substitute a number for a variable and evaluate the expression. Algebraic Expression “Take some number and add 4.” x+4 Algebraic Expression Evaluate x + 4 when x = 9. x+4 Substitute 9 + 4 = 13 Example a) Evaluate y ÷ 4 when y = 24. b) Evaluate 7n when n = 3. So… What Did You Intend to Say? “I saw the man with the binoculars.” “They are hunting dogs.” “Police help dog bite victim.” “Wanted: a nurse for a baby about twenty years old.” “I once saw a deer riding my bicycle.” “Look at the dog with one eye.” en.wikipedia.org/wiki/List_of_linguistic_example_sentences#Syntactic_ambiguity So… What Did You Intend to Say? “"Turn right after going straight and then left".” So… What Did You Intend to Say? 6−4+2 So… What Did You Intend to Say? 6 − (4 + 2) The Order of Operations When reading a numerical expression, we agree to perform operations in the following order: 1) Perform operations inside Parentheses 2) Evaluate numbers with Exponents 3) Multiply and Divide from left to right 4) Add and Subtract from left to right The Order of Operations A “common” mnemonic for remembering this order: Example Evaluate each expression using the order of operations. a) 17 − 4 • 2 d) 5 • 11 − 2 b) 12 + 12 ÷ 3 e) 92 − 1 + 4 c) 13 − (4 − 2)3 + 2 Example Evaluate each expression using the order of operations. a) 17 − 4 • 2 d) 5 • 11 − 2 b) 12 + 12 ÷ 3 e) 92 − 1 + 4 c) 13 − (4 − 2)3 + 2 f) 15 − (28 ÷ (7 − 3)) Example Evaluate each expression using the given substitution. a) 3(x + 4) when x = 6 b) 12 + n2 when n = 3 c) 9 + 3(y ÷ 4) when y = 12 Example Write a numerical expression that uses the order of operations to represent each problem. a) Divide 33 by the sum of 8 and 3. b) Subtract the difference of 6 and 4 from 12. c) Add the square of 7 to the sum of 4 and 6. Example You work a part-time job that pays $11 an hour. Write an algebraic expression that represents the total amount of money you’ve made in terms of hours worked. Example You have a part-time job that pays $16 per hour. You receive a paycheck with a gross amount of $512. How many hours did you work? Homework #9 - §4.3 Pages 150-153 #7, 9, 16, 18, 20, 24, 26, 28, 31, 39 (Just determine whether the answer is correct or incorrect and why or why not)