Chapter 1: Sets, Operations and Algebraic Language
TEACHER
1.7: Order of Operations
The PEMDAS Pyramid (Please excuse my dear aunt Sally’s Labrador Retriever.”)
P
E
M
A
D
S
(LEFT TO RIGHT)
Level 1
P
Perform any operations inside grouping symbols such as parenthesis,
brackets, and absolute value signs. When a fraction bar is involved, add
parentheses around the numerator and around the denominator.
Level 2
E
Level 3
M&D
Simplify any terms with exponents.
Level 4
A&S
Perform any operations involving addition and subtraction.
In levels 3 and 4, if there are two or more operations on the same level of the
pyramid, start with the operation that is furthest left and proceed to the right.
Perform any operations involving multiplication and division.
Sample Problem
The expression 15 – 3[2 + 6(–3)] simplifies to
(1) –45
(3) 63
(2) –33
(4) 192
The first step is the inner-most parenthesis
15 - 3[2 + 6(-3)]
15 - 3[2 + (-18)]
The next step is still in the inner parentheses
15 - 3[2 + (-18)]
15 - 3[-16]
Now we have a choice between multiplication and subtraction. Multiplication comes
first.
15 - 3[-16]
15 +48
Now all we have left is the addition: 15+48=63
1
Chapter 1: Sets, Operations and Algebraic Language
TEACHER
1.7: Order of Operations
Correct Order of
Operations
Correct
Incorrect Order of
Operations
Wrong
6 × (5 + 3) = 6 × 8 = 48
6 × (5 + 3) = 30 + 3 = 33
(wrong)
2 + 5 × 3 = 2 + 15 = 17
2 + 5 × 3 = 7 × 3 = 21
(wrong)
5 × 22 = 5 × 4 = 20
5 × 22 = 102 = 100
(wrong)
30 ÷ 5 × 3 = 6 × 3 = 18
30 ÷ 5 × 3 = 30 ÷ 15 = 2
REGENTS QUESTIONS
1
(wrong)
SOLUTIONS
(3)
6
is Using the acronym PEMDASLR
2
indicates that addition and subtraction
evaluated, what would be done last?
operations should be performed from
(1) subtracting
(3) adding
left to right. Since the addition is to the
(2) squaring
(4) dividing
right of the subtraction, the addition
would be done last.
If
the
expression
3  42 
(4)
2
What is the first step in simplifying
the expression (2  3  4  5) 2 ?
(1) square 5
(2) add 4 and 5
(3) subtract 3 from 2
(4) multiply 3 by 4
3
The expression 15 – 3[2 + 6(–3)]
simplifies to
(1) –45
(3) 63
(2) –33
(4) 192
15 – 3[2 + 6(–3)]
15 – 3[2 + (-18)]
15 – 3[-16]
15 + 48
63
4
On February 18, from 9 a.m. until 2
p.m., the temperature rose from –14°F
(1)
36 – (-14) = 50
2
Using the acronym PEMDASLR
indicates that operations inside the
expression’s parentheses should be
performed first. Multiplication precedes
addition.
(3)
Chapter 1: Sets, Operations and Algebraic Language
TEACHER
1.7: Order of Operations
to 36°F. What was the total increase in
Perhaps the easiest Regents question ever,
temperature during this time period?
requiring only the subtraction of two
(1) 50°
(3) 32°
integers.
(2) 36°
(4) 22°
3