Order of Operations

Algebra Standard GLE Understand and Use Order of Operations SPI Evaluate multi-step numerical expressions involving fractions using order of operations. CCSS Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

Order of Operations Why use Order of Operations???

Do both sentences mean the same? The teacher said, “The student is wrong.” “The teacher,” said the student, “is wrong.”

“In mathematical expressions, what would have the same type of effect as punctuating a sentence?” 22 + (12 x 2) = = 46 ( ) x 2 = 34 x 2 = 68 How does a parenthesis change the evaluation of the expression?

Evaluate: x 2 Is the answer 18 or 13? The order of operations become important. “What if there are no parentheses in an expression? How do we evaluate it?”

Order of Operations Just as it is important for you to add your items when you are shopping first before adding sales tax, it is equally important to solve expressions involving more than one operation in a certain order. When evaluating expressions with more than one operation, you should use the order of operations.

We have an order to evaluating an expression The order of operations is a set of rules used for evaluating an expression with more than one operation.

Order of Operations “Please Excuse My Dear Aunt Sally” (PEMDAS) is a way to help remember how to perform the order of operations. 1st: Work within the parentheses 2nd: Exponents 2 ¶ = 2x2x2x2x2 = 32 3rd: Multiplication & division from left to right 4th: Addition & subtraction from left to right

Order of Operations Example 1 Evaluate this expression: 14 – 6  3 Strategy: Use the order of operations. Step 1: There are no grouping symbols or exponents, so multiply and divide from left to right. 14 – 6  3 14  2 Step 2: Add and subtract from left to right. 14  2 12 Solution 14  6  3  12

Priority of Operations Parenthesis Exponents Multiplication/Division Addition/Subtraction

Group Activity Distribute one card to each participant Solve the expression Circulate and find a partner with an equivalent expression Explain to partner order used to evaluate the expression

Priority of Operations ( ) Please x 2 Excuse x,  My Dear +, - Aunt Sally

Example : Evaluate ÷ (8 - 3) x Step 1: ÷ (8 - 3) x = ÷ 5 x Parentheses Step 2: ÷ 5 x = x Division Step 3: x = Multiplication Step 4: = Subtraction Step 5: = 13 Addition

PEMDAS Colored-coded (5 - 4) x 22 1 x (3 x 4)

Identify the steps in different colors. Second, complete each step in that color – 5 x 10 Â – 50 Â – – 25 5

Dr. Xpression Operation! Solve each expression Cut out the expression an glue under the equivalent expression to match

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Your Turn!!! Solve these expressions using the order of operations. 1) x 2 2) (2 + 6) 3) (4 - 2) + 6 4) 2 x 9 - 3(6 - 1) + 1 5) ÷ 4 x 2

1) 6 2) 34 3) 36 4) 4 5) 20 Check Your Answers