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Order of Operations 1.3 Goal Use the established order of operations. Key Words order of operations left-to-right rule

ORDER OF OPERATIONS In algebra there is an order of operations to evaluate an expression involving more than one operation. Order of Operations 1.First do operations that occur within grouping symbols. ( ) ; [ ] ; { } 2.Then evaluate powers. 3.Then do multiplications and divisions from left to right. 4.Finally, do additions and subtractions from left to right. 1.3 Order of Operations Please Excuse My Dear Aunt Sally. PEMDAS L  R L  R

1.3 Order of Operations EXAMPLE 1 Evaluate Without Grouping Symbols Evaluate the expression 3x when x = 4. Use the order of operations. Solution 3x · Substitute 4 for x 3 · Evaluate power Multiply 3 times 16 49Add

1.3 Order of Operations Checkpoint Evaluate the variable expression when x = 2. Use the order of operations.

EXAMPL E 2 Use the Left-to-Right Rule Evaluate the expression using the left-to-right rule. a.24 – 8 – 6 (24 – 8) - 6 Work from left to right. 16 – 6 10 b. 15 · 2 ÷ 6 (15 · 2) ÷ 6 Do multiplication first. 30 ÷ 6 5

EXAMPL E 2 Use the Left-to-Right Rule c · 2 – 3

EXAMPL E 3 Expressions with Fraction Bars A fraction bar can act as a grouping symbol: Evaluate the expression: Then simplify the answer.

Checkpoint Use the order of operations and Left-to- Right Rule. Evaluate the variable expression when x = 1.

Checkpoint Use the order of operations and Left-to- Right Rule. Evaluate the variable expression when x = 1.

EXAMPL E 4 Use a Calculator Enter the following in your calculator. Does the calculator display 6 or 1? ÷ - Most calculators are programmed to use order of operations. If it uses the order of operations – the answer will be 6.

EXAMPL E 5 Evaluate a Real-Life Expression BASKETBALL SCORES You are playing basketball. You make 8 field goals and 2 free throws. Your friend makes half as many field goals as you and no free throws. How many points ahead of your friend are you?

Checkpoint Evaluate a Real-Life Expression Your friend makes 4 field goals. You make three times as many field goals as your friend plus one field goal. How many points do you have? Explain the order of operations you followed.

Evaluate the expression 4x 2 – 8 when x = 3. Use the order of operations. Evaluate the expression using the left-to- right rule. a. 32 – b. 48 ÷ 3 · 2 c ÷ 3 – 3

Evaluate the expression. Then simplify the answer. When you enter the following in your calculator, does the calculator display 5.8 or 1.3? Example 3Example ÷ - ENTER