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1-1 Order of Operations
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The following expression represents
Joe's grade in math:
150 - 100 ÷ 2
Should Joe be happy with his grade?
Why or why not?
1-1 Order of Operations
Learn to use the order of operations to
simplify numerical expressions.
1-1 Order of Operations
A numerical expression is an expression
made up of numbers and operations
Order of operations are the rules used to
simplify a numerical expression
1-1 Order of Operations
Why do we need the order of operations?
Joe’s math grade:
150 - 100 ÷ 2
150 – 100 ÷ 2
50 ÷ 2
25
150 – 100 ÷ 2
150 - 50
100
In mathematics there are often options for what order you
can simplify expressions. However, there is a system that
ALWAYS works and will give you the correct answer.
1-1 Order of Operations
P arenthesis
E xponents
M ultiplication
D ivision
A ddition
Subtraction
From left to right
From left to right
1-1 Order of Operations
Reminders
*when there is more than one set of parenthesis,
complete the inside first
*complete multiplication and division from left to
right
*complete addition and subtraction from left to
right
1-1 Order of Operations
The term 27 is called a power. If a number
is in exponential form, the exponent
represents how many times the base is to
be used as a factor.
Exponent
Base
2
7
=2222222
1-1 Order of Operations
Example A:
Simplify the expression.
23
32
52
222
33
55
8
9
25
1-1 Order of Operations
Example B:
Simplify the expression. Use the order of
operations to justify your answer.
3 + 15 ÷ 5
3 + 15 ÷ 5
3+3
6
Divide.
Add.
1-1 Order of Operations
Example C:
Simplify the expression. Use the order of
operations to justify your answer.
44 – 14 ÷ 2 · 4 + 6
44 – 14 ÷ 2 · 4 + 6
44 – 7 · 4 + 6
44 – 28 + 6
16 + 6
22
Divide and multiply from
left to right.
Subtract and add from
left to right.
1-1 Order of Operations
Example D:
Simplify the expression. Use the order of
operations to justify your answer.
3 + 23 · 5
3 + 23 · 5
Evaluate the power.
3+8·5
Multiply.
3 + 40
43
Add.
1-1 Order of Operations
Example E:
Simplify the expression.
2 (3 · 4) ÷ 6
2(3*4)÷6
2 (12 ) ÷ 6
24 ÷ 6
4
Parenthesis.
Multiply and Divide from
left to right.
1-1 Order of Operations
Example F:
Simplify the expression.
[(26 – 4 · 5) + 6]2
[(26 – 4 · 5) + 6]2
[(26 – 20) + 6]2
[6 + 6]2
122
144
The parentheses are
inside the brackets, so
perform the operations
inside the parentheses
first.
1-1 Order of Operations
Check your understanding:
1. 43 + 16 ÷ 4
2. 28 - 4 · 3 ÷ 6 + 4
3. 25 – 42 ÷ 8
4. (32 + 11) ÷ 5
5. 10 – [4(25 +1)] ÷ 2
6. 32 + 6(4 – 22) + 8
1-1 Order of Operations
Lesson Quiz
Simplify each expression.
1. 27 + 56 ÷ 7
35
2. 9 · 7 – 5
58
3. (28 – 8) ÷ 4
5
4. 136 – 102 ÷ 5
116
5. (9 – 5)3 · (7 + 1)2 ÷ 4
1,024
1-1 Order of Operations
Lesson Quiz
Evaluate.
6. Denzel paid a basic fee of $35 per month plus
$2 for each phone call beyond his basic plan.
Simplify the expression 35 + 8(2) to find how
much Denzel paid for a month with 8 calls
beyond the basic plan.
$51
1-1 Order of Operations
Lesson Quiz
7. Simplify the expression 36 + 63 ÷ 9.
A. 11
B. 36
C. 27
D. 43
1-1 Order of Operations
Lesson Quiz
8. Simplify the expression 3  6 – 12.
A. 12
B. 36
C. 24
D. 42
1-1 Order of Operations
Lesson Quiz
9. Simplify the expression (36 – 6) ÷ 15.
A. 15
B. 10
C. 12
D. 2
1-1 Order of Operations
Lesson Quiz
10. Simplify the expression
(8 – 3)3  (9 + 1)2 ÷ 5.
A. 1,000
B. 1,500
C. 2,000
D. 2,500
1-1 Order of Operations
Lesson Quiz
11. Robert paid a $200 basic fee plus $70 a
day to get his house painted. Simplify the
expression 200 + 90(7) to find how much
it cost him if it took 9 days to complete the
painting.
A. $830
B. $1260
C. $1740
D. $2030