4 3 Order of Operations 021617 Today Well

§ 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 7 n 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 + n 2 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)