Transcript Order of Operations - Texas Collaborative

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:
12  3  4
9+4
13
14  7  3  6
21 – 3 + 6
18 + 6
24
Remember, grouping
symbols then addition OR
subtraction as you come to
it from left to right.
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
Multiplication and Division
12  3(4)  1
We no longer have only addition and
subtraction. We must do any multiplication or
division BEFORE we do addition or subtraction.
12  3(4)  1
12  12  1
0 1
1
Try these. When you are finished, click on your answer choice.
7 1 3 2
18
12  6  2
3
6
12
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.
42  2  3
7
63
Try again!
42  2  3
Did you get 63 this time?
Great!
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.
56  4  2
What is your answer?
You should get 28,
56  4  2
14  2
28
Work these examples on your paper:
12 3(4)
4(4)
16
36  3  4  2
36  3  4  2
12  4  2
48  2
24
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
12  3  7  2  8
9
49  7  4  8
39
10  5(2)
4
Need to try
again? Study
these examples
first.
12  3  7  2  8
12  3  14  8
15  14  8
1 8
9
49  7  4  8
7  4 8
7  32
39
10  5(2)
2( 2)
4
Practice Problems
2(4)  6(5)  8
16  4  4  5  2
Remember the order:
1) Multiplication or
division from left to
right
2) Addition or
subtraction in order
from left to right
Solutions:
2( 4)  6(5)  8
8  30  8
38  8
46
16  4  4  5  2
4  20  2
4  10
14
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. Exponents
3. Multiplication OR Division
4. 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)