Oder of Operations - PEMDAS/ GEMDAS

2. Order Of
OperatiOn
s

3. In most languages, the meaning
of words depend on the order.
Example:
Sign the check
is not the same as
Check the sign

4. When you make cereal, do you fill
the bowl with milk or cereal first?
Why?

5. When you get dressed, do you put on
your shoes or socks first? Why?

6. In our lives and in math,
we need to do things in a
certain order to make
sure they turn out right.

7. That is where the
ORDER OF
OPERATIONS
come into play!

8. Try to come up with two or
more examples from your
life. And share it with the
class.

9. Evaluate 7 + 4 • 3
You can get 2 different answers
depending on which operation you
did first. We want everyone to get
the same answer so we must follow
the order of operations.
Is your answer 33 or 19?

10. Menu
P.E.M.D.A.S.
Quiz
Practice
Home
What does
order of
operations
mean?

11. The Order of
Operations tells us
how to do a math
problem with more
than one operation,
in the correct order.

12. What does order of
operations mean?
• Order of operations is the order in which
you solve a math problem with many
components.
• The rule for order of operations is what we
called P.E.M.D.A.S.
• Don’t forget to solve the problem
from left to right!

13. Please Excuse
My Dear Aunt
Sally
This will help you
to remember the
order of
operations.

14. Important Vocabulary
• A numerical expression is a
mathematical phrase that includes only
numbers and operation symbols.
• When you simplify a numerical
expression, you are finding its value.
Numerical
Expressions
4 + 8 ÷ 2 ×
6
371 – 203 + 2 5,006 × 19

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16. ORDER OF OPERATIONS
1. Parentheses - ( ) or [ ]
2. Exponents or Powers
3. Multiply and Divide (from left to right)
4. Add and Subtract (from left to right)

17. Parentheses
•Perform calculations inside parentheses
first.
Ex. (3 x 6) = 18
Sol. (3 x 6) + 2 = 20

18 + 2 = 20

18. Exponents
•The second step of the order of
operations is exponents.
Ex. (3 + 2)2
= 25

52
= 25
Sol. 3 + (3 + 2)2
= 28

3 + 25 = 28

19. Multiplication and Division
Perform all multiplication & division from
left to right…
Multiplication and Division are married 
Ex. 6 x 4 = 24
Sol. (3-2)2
x 4 = 4

1 x 4 = 4

20. Multiplication and Division
Perform all multiplication & division from
left to right…
Multiplication and Division are married 
Ex. 8 ÷ 2 = 4
Ex. 8 ÷ 2 + (3 x 6) = 22

4 + 18 = 22

21. Addition and Subtraction
Perform all addition and subtraction from
left to right..
Addition and Subtraction are also married 
Ex. 3 + 6 = 9
Ex. 3 + 4 ÷ 2 = 4

3 + 2 = 4

22. Addition and Subtraction
Perform all addition and subtraction from
left to right..
Addition and Subtraction are also married 
Ex. 16 – 4 = 12
Ex. 18 – (2 + 2)2
= 2

18 - 16 = 2

23. COMMON ERROR!
Be Careful!
PEMDAS is only FOUR STEPS!
P – E – MD – AS
It is NOT six steps!
P – E – M – D – A – S

25. LetLet’’s Try Somes Try Some
 Problems!Problems!
GET YOURSELFGET YOURSELF
READY!!READY!!

26. PEMDAS
14+2- (9+1)
14+2- 10
16 - 10
6

27. PEMDAS
3 x (9+1)
3 x(10)
3 x 10
30

28. PEMDAS
4+5 x (6-2)
4+5 x 4
4+20
24

29. PEMDAS
64 ÷ (9 x 3-19)
64÷(27 –19)
64 ÷ 8
8

30. WANT MORE?WANT MORE?

Get yourself ready for the secondGet yourself ready for the second
time!!time!!

31. Example #5
14 ÷ 7 • 2 - 3
= 2 • 2 - 3 (Divide l/r.)
= 4 - 3 (Multiply.)
= 1 (Subtract.)

32. Example #6
3(3 + 7) 2
÷ 5
= 3(10) 2
÷ 5 (parentheses)
= 3(100) ÷ 5 (exponents)
= 300 ÷ 5 (multiplication)
= 60 (division)

33. Example #7
20 - 3 • 6 + 102
+ (6 + 1) • 4
= 20 - 3 • 6 + 102
+ (7) • 4 (parentheses)
= 20 - 3 • 6 + 100 + (7) • 4 (exponents)
= 20 - 18 + 100 + (7) • 4 (Multiply l/r.)
= 20 - 18 + 100 + 28 (Multiply l/r.)
= 2 + 100 + 28 (Subtract l/r.)
= 102 + 28 (Add l/r.)
= 130 (Add.)

34. Which of the following represents
112
+ 18 - 33
· 5 in simplified form?
1. -3,236
2. 4
3. 107
4. 16,996
Answer Now

35. Simplify
16 - 2(10 - 3)
Answer Now
1. 2
2. -7
3. 12
4. 98

36. Simplify
24 – 6 · 4 ÷ 2
Answer Now
1. 72
2. 36
3. 12
4. 0

37. IMPORTANT!!
ALWAYS UNDERLINE the portion of the
problem you are solving and BRING
DOWN the remaining parts of the
problem!
Your problem should
look like an upside
down triangle!!

38. WANT MOREWANT MORE
AND MORE?AND MORE?

Get yourself ready for the thirdGet yourself ready for the third

39. PEMDAS
Where would you put your
Parentheses ( ) to make
this problem true?
6 x 8 - 5 = 18
6 x (8 - 5)= 18
6 x 3 = 18

40. PEMDAS
Where would you put your
Parentheses ( ) to make this
problem true?
42 ÷ 2 x 3 - 5 = 2
42 ÷ (2 x 3) - 5 = 2
42 ÷ (6) - 5 = 2
42 ÷ 6 - 5 = 2
7 - 5 = 2

41. PEMDAS
Get your
whiteboards
ready!

42. Practice
(3 + 5)2
– 2 =28 – 32
x 2 =
3 + 8 ÷ 4 + 12 =(3 + 5) – 2 =
Answers
Copy the following problems into your
notebook and practice them.

43. Practice
42
+ (2 x 5) x 3 – 6 ÷ 2 =
Answers
Copy the following problems into your
notebook and practice them.
(3 x 2)2
÷ 5 – 3 + 4 =

44. PEMDAS
Now we are going to
get in our math groups
to work on a
worksheet.

45. Have fun doingHave fun doing
the Order ofthe Order of
Operations!Operations!

46. Quiz
12 x 2 – 4 x 6 =
Copy the following problems on a piece of paper and
hand them in when you are done.
(12 + 2) – 12 ÷ 22
x 1 =
Answer

47. (3 x 2)2
x 4 ÷ 2 + 32
– 4 =
Copy the following problems on a piece of paper and
hand them in when you are done.
(12 + 2) – 12 ÷ 22
x 1 =
Answer

48. Credits
Graphics from:
Microsoft Office Online
Website from practice help: Math
Goodies
http://www.mathgoodies.com/lessons/vol7
/order_operations.html

49. Objective:
• To give students a better understanding of the
order of operations.
▪Practice problems and quizzes are included to
assist in the lesson.
Audience:
•Fourth to sixth grade.

50. 1. substitute the given numbers for each
variable.
2. use order of operations to solve.
Evaluating a Variable Expression
To evaluate a variable expression:

51. Example # 4
n + (13 - n) ÷ 5 for n = 8
= 8 + (13 - 8) ÷ 5 (Substitute.)
= 8 + 5 ÷ 5 (parentheses)
= 8 + 1 (Divide l/r.)
= 9 (Add l/r.)

52. Example # 5
8y - 3x2
+ 2n for x = 5, y = 2, n =3
= 8 • 2 - 3 • 52
+ 2 • 3 (Substitute.)
= 8 • 2 - 3 • 25 + 2 • 3 (exponents)
= 16 - 3 • 25 + 2 • 3 (Multiply l/r.)
= 16 - 75 + 2 • 3 (Multiply l/r.)
= 16 - 75 + 6 (Multiply l/r.)
= -59 + 6 (Subtract l/r.)
= -53 (Add l/r.)

53. What is the value of
-10 – 4x if x = -13?
Answer Now
1. -62
2. -42
3. 42
4. 52

54. What is the value of
5k3
if k = -4?
Answer Now
1. -8000
2. -320
3. -60
4. 320

55. What is the value of
if n = -8, m = 4, and t = 2 ?
Answer Now
t
mn2 +
1. 10
2. -10
3. -6
4. 6