The Order of Operations

1
The Order of Operations
Lesson 1.1.3
2
Lesson 1.1.3
The Order of Operations
California Standard Algebra and Functions 1.2
What it means for you
Youll learn about the special order to follow
when youre deciding which part of an expression
to evaluate first.
Use the correct order of operations to evaluate
algebraic expressions such as 3(2x 5)2.
Key Words

• Parentheses
• Exponents
• PEMDAS

3
Lesson 1.1.3
The Order of Operations
When you have a calculation with more than one
operation in it, you need to know what order to
do the operations in.
E.g. if you evaluate the expression 2 3 7 by
doing
youll get a different answer from someone who
does
So the order you use really matters.
Theres a set of rules to follow to make sure
that everyone gets the same answer. Its called
the order of operations and youve seen it
before in grade 6.
4
Lesson 1.1.3
The Order of Operations
The Order of Operations is a Set of Rules
An expression can contain lots of operations.
When you evaluate it you need a set of rules to
tell you what order to deal with the different
bits in.
Order of operations the PEMDAS Rule
()
First do any operations inside parentheses.
Parentheses
x2 y7
Exponents
Then evaluate any exponents.

Multiplication or Division
Next follow any multiplication and division
instructions from left to right.
Finally follow any addition and subtraction
instructions from left to right.
Addition or Subtraction

5
Lesson 1.1.3
The Order of Operations
When an expression contains multiplication and
division, or addition and subtraction, do first
whichever comes first as you read from left to
right.
Divide first, then multiply.
9 4 3
Multiply first, then divide.
9 4 3
9 4 3
Add first, then subtract.
9 4 3
Subtract first, then add.
Following these rules means that theres only one
correct answer. Use the rules each time you do a
calculation to make sure you get the right answer.
6
Lesson 1.1.3
The Order of Operations
You Can Also Use GEMA For the Order of Operations
GEMA is another way to remember the order of
operations
First evaluate anything grouped by parentheses,
fraction bars or brackets
()
Grouping
x2 y7
Exponents
Then evaluate any exponents.

Multiplication or Division
Next follow any multiplication and division
instructions from left to right.
Finally follow any addition and subtraction
instructions from left to right.
Addition or Subtraction

You can use either PEDMAS or GEMA whichever one
you feel happier with.
7
Lesson 1.1.3
The Order of Operations
Example 1
What is 8 4 4 3?
Solution
8 4 4 3
There are no parentheses or exponents
You do the division first as it comes before the
multiplication, reading from left to right.
Do the division first
2 4 3
Then the multiplication
8 3
Finally do the addition to get the answer
11
Solution follows
8
Lesson 1.1.3
The Order of Operations
Guided Practice
Evaluate the expressions in Exercises 16.
1. 3 2 6 1 3. 4 3 2 7 5. 40 10 5
6
2. 6 2 1 4. 2 5 10 6. 5 10 10
4
6
12
52
28
6

Solution follows
9
Lesson 1.1.3
The Order of Operations
Always Deal with Parentheses First
When a calculation contains parentheses, you
should deal with any operations inside them
first.
2(4 52) 1
2(4 52) 1
You still need to follow the order of operations
when youre dealing with the parts inside the
parentheses.
2(4 25) 1
2(100) 1
10
Lesson 1.1.3
The Order of Operations
Example 2
What is 10 2 (10 2)?
Solution
The order of operations says that you should deal
with the operations in the parentheses first
thats the P in PEMDAS.
10 2 (10 2)
First write out the expression
Do the addition in parentheses
10 2 12
You do the division first here because it comes
first reading from left to right.
5 12
Then do the division
60
Finally do the multiplication
Solution follows
11
Lesson 1.1.3
The Order of Operations
Guided Practice
Evaluate the expressions in Exercises 714.
7. 10 (4 3) 9. 10 (7 5) 11. 10 (2 4)
3 13. 6 (8 4) 11
8. (18 3) (2 3 4) 10. 41 (4 2
3) 12. (5 7) (55 11) 14. 32 2 (16 2)
3
20
5
38
57
10
23
48
Solution follows
12
Lesson 1.1.3
The Order of Operations
PEMDAS Applies to Algebra Problems Too
The order of operations still applies when you
have calculations in algebra that contain a
mixture of numbers and variables.
Do the addition in parentheses, then the
multiplication
3 (2 4)
Do the addition in parentheses, then the
multiplication
a (2 4)
Do the addition in parentheses, then the
multiplication
3 (b 4)
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Lesson 1.1.3
The Order of Operations
Example 3
Simplify the calculation k (5 4) 16 as far
as possible.
Solution
k (5 4) 16
First write out the expression
Do the addition in parentheses
k 9 16
9k 16
Then the multiplication
Solution follows
14
Lesson 1.1.3
The Order of Operations
Guided Practice
Simplify the expressions in Exercises 1520 as
far as possible.
15. 5 7 x 17. 3 (y 2) 19. 20 (4 2)
t
16. 2 a 4 1 18. 10 (3 2) r 20. p 5
(2 m)
5 7x
4a 1
3y 6
2 r
8t 20
p 10 5m
Solution follows
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Lesson 1.1.3
The Order of Operations
Independent Practice
1. Alice and Emilio are evaluating the expression
5 6 4. Their work is shown
below. Explain who has the right answer.
Alice 5 6 4 11 4 44
Emilio 5 6 4 5 24 29
Emilio has the right answer because he has used
the correct order of operations he has done the
multiplication before the addition.
Solution follows
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Lesson 1.1.3
The Order of Operations
Independent Practice
The local muffler replacement shop charges 75
for parts and 25 per hour for labor. 2. Write
an expression with parentheses to describe the
cost, in dollars, of a replacement if the job
takes 4 hours. 3. Use your expression to
calculate what the cost of the job would be if it
did take 4 hours.
75 (4 25)
175
Solution follows
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Lesson 1.1.3
The Order of Operations
Independent Practice
Evaluate the expressions in Exercises 47.
4. 2 32 8 2 5 6. 7 5 (10 6 3)
5. 4 7 3 7. 3 (5 3) (27 3)
4
25
47
15
8. Paul buys 5 books priced at 10 and 3 priced
at 15. He also has a coupon for 7 off his
purchase. Write an expression with parentheses to
show the total cost, after using the coupon, and
then simplify it to show how much he spent.
(5 10) (3 15) 7. He spent 88.
Solution follows
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Lesson 1.1.3
The Order of Operations
Independent Practice
9. Insert parentheses into the expression 15 3
6 4 to make it equal to 48.
(15 3 6) 4
Simplify the expressions in Exercises 1012 as
far as possible.
10. x 7 2 11. y x (4 3) y 12. 6 (60
x 3)
x 14
7x
66 3x
Solution follows
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Lesson 1.1.3
The Order of Operations
Round Up
If you evaluate an expression in a different
order from everyone else, you wont get the right
answer. Thats why its so important to follow
the order of operations.
This will feature in almost all the math you do
from now on, so you need to know it.
Dont worry though just use the word PEMDAS or
GEMA to help you remember it.