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**Order of Operations What to do first?????**

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**Instructions for Tutorial**

View the slide show and answer the questions as you go. Many slides will change as you continue to click while viewing them so it is important that you not skip around the slides. When you are ready for the next piece of information, “left click” your mouse or type “enter” on the keyboard.

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What are operations? In mathematics, there are several operations. You are very familiar with the four basic ones: Adding Subtracting Multiplying Dividing

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In an expression where there is more than one operation, the value of an expression will depend upon the order in which you perform these operations. There are several rules which we all agree to follow so that we will all reach the same answer for a problem. In this presentation, we will consider multiplication, division and grouping symbols and summarize the rules at the end.

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**Addition and Subtraction**

Remember, First: we always perform operations within grouping symbols Second: expressions involving exponents need to be simplified before using them in calculations Then: when the problem involves ONLY addition and subtraction, you perform those operations as you come to them, reading from left to right.

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**Work these examples on your paper:**

Remember, grouping symbols then addition OR subtraction as you come to it from left to right. 9 + 4 13 21 – 3 + 6 18 + 6 24

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**Consider: There are 3 operations here. Can you identify them?**

They are: subtraction: 12 – 3(4) multiplication: 3 (4) addition: 3(4) + 1

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**Multiplication and Division**

We no longer have only addition and subtraction. We must do any multiplication or division BEFORE we do addition or subtraction.

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**Try these. When you are finished, click on your answer choice.**

Remember, First: grouping symbols and exponents as needed Second: multiplication OR division as you come to it from left to right Last: addition OR subtraction as you come to it from left to right.

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OOPS! Do multiplication or division as you come to it reading from left to right. THEN go back and do any addition or subtraction as you come to it reading from left to right. Click here to try again

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**Try these. When you are finished, click on your answer choice.**

Remember, First: grouping symbols and exponents as needed Second: multiplication OR division as you come to it from left to right Last: addition OR subtraction as you come to it from left to right.

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When problems involve multiplication and division, we perform the first of either that we reach as we move from left to right—just like reading a book. Apply this rule by evaluating this expression. Click on your answer choice. 7 63

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OOPS!! You did the multiplication first. Remember, we do multiplication OR division as we come to it from left to right. Here you reach the division first, so you do it first. Yes, “please excuse my dear aunt sally” says “my dear” or multiplication division. However, multiplication and division are same level operations. And Aunt Sally does not want us to do all the multiplication and then all the division (really, she doesn’t). Note: you should remember that dividing by a fraction is accomplished by multiplying by the reciprocal. Try Again!

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Try again! Did you get 63 this time? Great!

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When problems involve multiplication and division, we perform the first of either that we reach as we move from left to right—just like reading a book. Apply this rule by evaluating this expression. What is your answer? You should get 28,

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**Work these examples on your paper:**

4(4) 16

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Nice work! You performed the subtraction first since you encountered it first as you moved from left to right. Click here to go back to the show!

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**CONGRATULATIONS! Here’s what we have learned:**

When a problem involves more than one operation, we use this order to simplify expressions: First, grouping symbols; and you must always simplify expressions with exponents before you can calculate with them. Next, multiplication OR division as you come to it reading from left to right. Last, addition OR subtraction as you come to it from left to right

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**Test Yourself Remember the order:**

1) Multiplication or division from left to right 2) Addition or subtraction in order from left to right 9 39 4

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**Need to try again? Study these examples first.**

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**Practice Problems Remember the order:**

1) Multiplication or division from left to right 2) Addition or subtraction in order from left to right

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Solutions:

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REMEMBER: When a problem involves more than one operation, we use this order to simplify expressions: First, grouping symbols; and you must always simplify expressions with exponents before you can calculate with them. Next, multiplication OR division as you come to it reading from left to right. Last, addition OR subtraction as you come to it from left to right

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**How to remember???? The order is usually stated as follows:**

Parentheses (Grouping Symbols) Exponents Multiplication OR Division Addition OR Subtraction There are two popular mnemonic devices to help you remember the order. Choose the one that works for you! PEMDAS Please Excuse My Dear Aunt Sally

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**Aunt Sally Straightened Out**

Please (P stands for parentheses and other grouping symbols) Excuse (E stands for exponents) My Dear (M and D for multiplication and division as you reach them reading from left to right) Aunt Sally (A and S for addition and subtraction as you reach them reading from left to right)

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Objectives 4 and 5 Order of operations ©2002 by R. Villar All Rights Reserved.

Objectives 4 and 5 Order of operations ©2002 by R. Villar All Rights Reserved.

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