Order of Operations

What to do first?????

Presentation 1

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

Consider:

12  3 ( 4 )  1 There are 3 operations here. Can you identify them?

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

The value of the 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 slide, we will look at the simplest problems first, progress to more difficult ones and summarize the rules at the end.

When problems involve addition and subtraction, 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.

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

9  5  2 2 6

When problems involve addition and subtraction, 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.

9  2  3 What is your answer? You should get 10, 9-2+3 7+3 10 Remember, addition OR subtraction as you come to it from left to right.

Work these examples on your paper: 12  3  4 9 + 4 14  13 7  3  21 – 3 + 6 6 18 + 6 24 Remember, addition OR subtraction as you come to it from left to right.

Parentheses and other Grouping Symbols Change Things.

• If there are symbols in the expression that group operations, do those first. For instance, try this problem (the parentheses group 5 + 2). Click on your answer choice. Be sure your sound is on!!

9  ( 5  2 ) 6 2

Work these examples on your paper: ( 12  3 ) 9 + 4  4 13 Remember, grouping symbols then addition OR subtraction as you come to it from left to right.

( 2  3 ) 5 – 2  ( 6  4 ) 3

Parentheses are not the only grouping symbols! Radicals are grouping symbols, too.

Try this problem. Choose the correct answer and you will hear the applause. If you don’t hear the applause, you need to try again!

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

5



12



3

4 8

Having trouble? Try the next slide for help. Compare the work you did to the way the examples are worked.

5  12  3

5



9 (radicals are grouping symbols, so perform the 12



3 first) 5



3 9



3 , since 3

2 

9 8 lastly, perform the addition

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

Parentheses and radicals are not the only grouping symbols! Brackets are grouping symbols, too.

• Try this problem. Choose the correct answer and you will hear the applause. If you don’t hear the applause, you need to try again!

• One note: when grouping symbols are “nested” (one inside the other), do the work in the innermost set of symbols first.

2  12   3  4   6  20 22 38

2  12   3  4   6  when there are " nested" symbols, do the 2  12  7  6  within innermost ones first the remaining grouping symbols, do addition Or subtractio n as you come to it 2  5  6  from left to right 2   a number next to a grouping symbol indicates multiplica tion 22 Remember, grouping symbols then addition OR subtraction as you come to it from left to right.

Absolute value symbols are also grouping symbols as are fractions bars (which indicate division).

Try these: 12  3   3  2  8  1 13 20 Remember, grouping symbols then addition OR subtraction as you come to it from left to right.

6 4  2 2 ( 3  5 )  2  8  7 1/5 2

12 12   3  3   3 ( 6   2 8 )  8  12  3  14 15  14 1 4  ( 3  5 )  2 2 2 4   8 8   7 2 4 12   8 2  7 12  7 10  2 5 Did you notice that we have to replace 2 2 with 4 before calculating the denominator?

Congratulations!!

Now you know, when a problem involves addition, subtraction and/or grouping symbols: • First, grouping symbols • then addition OR subtraction as you come to it from left to right You must always simplify expressions with exponents before you can calculate with them.