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

Presentation 2

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.

What are operations?

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

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.

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.

Work these examples on your paper:

4312

63714

9 + 4

13

21 – 3 + 6

18 + 6

24

Remember, grouping symbols then addition OR subtraction as you come to it from left to right.

Consider:

1)4(312 There are 3 operations here. Can you identify them?

They are: subtraction: 12 – 3(4)

multiplication: 3 (4)

addition: 3(4) + 1

Multiplication and Division

1)4(312 We no longer have only addition and subtraction. We must do any multiplication or division BEFORE we do addition or subtraction.

1

10

11212

1)4(312

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

2612

2317

18 6 12

3 9

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.

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

3242

Try again!

Did you get 63 this time?

Great!

3242

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,

2456

28

214

2456

Work these examples on your paper:

)4(312

24336

4(4)

16

24

248

2412

24336

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

Test Yourself

• Remember the order:• 1) Multiplication or

division from left to right

• 2) Addition or subtraction in order from left to right

)2(510

84749

827312

39

4

9

Need to try again? Study these examples first.

4

)2(2

)2(510

39

327

847

84749

9

81

81415

814312

827312

Practice Problems

254416

8)5(6)4(2

Remember the order:1) Multiplication or division from left to right2) Addition or subtraction in order from left to right

Solutions:

14

104

2204

254416

46

838

8308

8)5(6)4(2

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

How to remember????The order is usually stated as follows:1. Parentheses (Grouping Symbols)2. Exponents3. Multiplication OR Division4. 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

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)