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Confidential3 Let's review what we learned in the last lesson.....
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Confidential 1
Today we will be learning about the
"Order of Operations"
Confidential 2
8 * 36 =
126 ÷ 6 =
29 * 5 =
42 ÷ 3 =
Let's do a few practice problems before we get started.
Confidential 3
Let's review what we learned in the last lesson.....
Confidential 4
Confidential 5
Confidential 6
A Numerical Expression is a combination of numbers and operations.
Examples: 4 + 3 * 5
22 + 6 ÷ 2
(10 * 8) - 7
1 2 34 56
Let's begin!
Confidential 7
Do you know what we mean by "Operations"?
We "operate " on the numbers by
Dividing
MultiplyingAdding
Subtracting+
-
÷x
1
2
3
4
5
67
8
9
Confidential 8
How might you solve this problem? 6 + 2 * 5 =
Could another student solve this problem differently?
6 + 2 * 5 =
How do we know which one is correct?????
Confidential 9
To find the correct answer, we need to follow an
Order of Operations
This tells us which operation to perform first so that everyone gets the same final answer!
Confidential 10
Order of Operations1.
Parentheses2. Exponents
3. Multiplication Division4. Addition Subtraction
Simplifying the expressionsinside grouping symbolsexamples: (3+5) or (4*6)Find the value of all powersexamples: 23 or 42
Perform multiplication or division in the order in which it occurs when reading the expression from left to right.
Perform addition or subtraction in theorder in which it occurs when reading the expression from left to right.
PEMDAS
Confidential 11
We can remember the Order of Operations as
PPEEMMDDAASSP E M D A Sarentheses
xponents
ultiplicationivisiondditionubtraction
"Please Excuse My Dear Aunt Sally"
Confidential 12
P E M D A Sarenthesesxponents
ultiplicationivisiondditionubtraction
Or
"Purple Eggplants Make Delicious Afternoon Snacks!"
Confidential 13
P E M D A Sarenthesesxponent
s ultiplicationivision
ddition ubtractio
n
Let's try some.....whichever comes first
whichever comes first
Numerical expression
4 + 3 * 5 =Read from left to right...just like a book.There are no Parentheses.There are no Exponents.There is some Multiplication so do this first.4 + 15
= We perform the Addition last.
19
Confidential 14
P E M D A Sarenthese
s
xponents
ultiplicatio
n ivision
dditionubtraction
whichever comes first whichever comes first
"Purple Eggplants Make Delicious Afternoon Snacks!"
10 - 2 + 8 =Read the expressionfrom left to right.
8 + 8 =We perform Addition and Subtraction in the order in which they occur.So do the Subtraction first!
Then do the Addition.16
Numerical Expression
Confidential 15
P E M D A Sarenthesesxponents
ultiplication
ivisiondditionubtraction
whichever comes first
whichever comes first
"Please Excuse My Dear Aunt Sally"
20 ÷ 4 + 17 * (9 - 6) =
Do the operations in Parentheses first.
20 ÷ 4 + 17 * 3 =
5 + 17 * 3 =
5 + 51 =56
There are no Exponents.
Perform Multiplication or Division in the order in which they occur.The Division should be done first.Then perform the Multiplication.Finally perform the Addition.
Confidential 16
Your turn!
10 + 2 x 15 =
25 x (5 - 2) ÷ 5
=
10 + (6 - 5) =
24 ÷ 23 + 6 =
PE
M
D
A
S
Confidential 17
Sometimes we have operations "nested" within the parentheses which must be completed first.
Example:60 ÷ (12 + 23) x 9 =60 ÷ (12 + 8) x 9 =
60 ÷ 20 x 9 =
3 x 9 =
27
We want to do the Parentheses but first we must take care of the Exponents WITHIN the Parentheses.
Then we can solve the Parentheses.Division comes before Multiplication when reading the expression from left to right.
Finally we can perform the Multiplication.
Confidential 18
Practice Problems
1) 9 + 3 - 5 =
2) (26 + 5) x 2 - 15 =
3) 18 ÷ (2 + 7) x 2 + 1 =
4) 52 + 8 ÷ 2 =
5) 10 - 3 + 9 =
6) 5 + (21 - 3) =
7) 21 ÷ (3 + 4) x 3 - 8 =
8) 19 - (32 + 4) + 6 =
Confidential 19
What is the value of 100 divided by 5 times 4 minus 79?
(Can you write this out as a "Numerical Expression"?)
Confidential 20
Can you develop an expression that usesmultiplication, division, addition, and subtraction,
as well as grouping symbols, whose solution is 2?????
Confidential 21
Adult admission to a football game is $5, and student
admission is $2. Which expression could be used tofind the total cost of 2 adult and 4 student
admissionsto the football game?
a.) 2 + $5 x 4 + $2b.) $5 + $2 + 6
c.) $2 + 4 x $5 + 2
d.) 2 x $5 + 4 x $2
Confidential 22
1.) Can you give me an example of a “ Numerical Expression“ ?
2.) What do I mean by "Operations“ ?
3.) In what order do I perform the "Operations“ ?
45 + 79 – (5 x3)
To operate on the numbers by using the rules of PEMDAS
ParenthesesP
E
M
D
A
S
Exponents
Multiplication
DivisionAddition
Subtraction
Your Your turnturn
Confidential 23
a.) 5 x 6 - (9 - 4) =
b.) 16 ÷ 2 + 8 x 3 =
c.) 43 - 24 + 8 =
d.) 45 ÷ 9 + 8 - 7 + 2 x 3 =
e.) (8 + 1) x 11 - 13 =
4.) Find the value of each expression?
Confidential 24
You did a GREAT job today!!!
*We learned to identify a "Numerical Expression".
4 + (8 x 2) - 3
* We learned about "Operations". + - ÷ x
* We learned that we need to perform "Operations" in a certain order.
Confidential 25
* We learned some funny ways to remember the "Order of Operations".
Please Excuse My Dear Aunt Sally!
Purple Eggplants Make Delicious Afternoon Snacks!
P
E
M
D
A
S
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
Confidential 26
You did a splendid Job
Be sure to practice what you have learned