Chapter 1: Sets, Operations and Algebraic Language
1.7: Order of Operations
The PEMDAS Pyramid
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
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Chapter 1: Sets, Operations and Algebraic Language
1.7: Order of Operations
Correct
Wong
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 = 102 = 100
(wrong)
30 ÷ 5 × 3 = 30 ÷ 15 = 2
(wrong)
5 × 22 = 5 × 4 = 20
30 ÷ 5 × 3 = 6 × 3 = 18
QUESTIONS
1
6
is evaluated, what would be done last?
2
(3) adding
(4) dividing
If the expression 3  42 
(1) subtracting
(2) squaring
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
4
On February 18, from 9 a.m. until 2 p.m., the temperature rose from –14°F to 36°F.
What was the total increase in temperature during this time period?
(1) 50°
(3) 32°
(2) 36°
(4) 22°
2
Chapter 1: Sets, Operations and Algebraic Language
1.7: Order of Operations
3