Order of Operations & Substitution Notes
Order of Operations
When simplifying expressions, you must do operations in a certain order to get correct answers. What is the acronym for this order?
So, we do any math inside of _____________ first. Then we simplify any _____________. Division and multiplication are like partners, and we do the one that comes first in the question. Addition and subtraction are like partners, and we do the one that comes first in the question.
When simplifying expressions, you must do operations in a certain order to get correct answers. What is the acronym for this order?
BEDMAS ­ brackets, exponents, division or multiplication, addition or subtraction
Within a bracket, we apply BEDMAS again.
Example
Simplify 2 + 3 x 4 ÷ 6
So, we do any math inside of BRACKETS first. Then we simplify any EXPONENTS. Division and multiplication are like partners, and we do the one that comes first in the question. Addition and subtraction are like partners, and we do the one that comes first in the question.
Within a bracket, we apply BEDMAS again. When doing a question, circle what to do in each step.
Example
Simplify 2 + 3 x 4 ÷ 6
Example
Simplify: 15 ­ 32 + 2(3 + 3 x 2)
2 + 12 ÷ 6
2 + 2
4
1
Order of Operations & Substitution Notes
Example
Simplify: 15 ­ 32 + 2(3 + 3 x 2)
15 ­ 32 + 2(3 + 6)
15 ­ 32 + 2(9)
15 ­ 9 + 2(9)
15 ­ 9 + 18
Example
You win the grand prize in the McDonald's draw, but have to answer the skill testing question first:
4 + (8 + 4 x 22) ÷ 6
6 + 18
24
Example
You win the grand prize in the McDonald's draw, but have to answer the skill testing question first:
4 + (8 + 4 x 22) ÷ 6
4 + (8 + 4 x 4) ÷ 6
4 + (8 + 16) ÷ 6
Example
Simplify: 7 + 2[20 ­ 2(32)]3 +10
4 + 24 ÷ 6
4 + 4
8
Example
Simplify: 7 + 2[20 ­ 2(32)]3 +10
7 + 2[20 ­ 2(9)]3 + 10
7 + 2[20 ­ 18]3 + 10
Substitution
7 + 2[2]3 + 10
7 + 2(8) + 10
7 + 16 + 10
33
2
Order of Operations & Substitution Notes
When substituting numbers in for variables, use brackets and then do BEDMAS.
Example
Simplify: a + a2b ­ b if a = 3 and b = 4
When substituting numbers in for variables, use brackets and then do BEDMAS.
Example
Simplify: a + a2b ­ b if a = 3 and b = 4
(3) + (3)2(4) ­ (4)
3 + 9(4) ­ 4
3 + 36 ­ 4
39 ­ 4
35
Example
Simplify if x = 6 and y = 2
Example
Simplify if x = 6 and y = 2
3x ­ 5y + (7y2 ­ 2xy) 3x ­ 5y + (7y2 ­ 2xy) 3(6) ­ 5(2) + (7(2)2 ­ 2(6)(2))
3(6) ­ 5(2) + (7(4) ­ 2(6)(2))
3(6) ­ 5(2) + (28 ­ 24)
3(6) ­ 5(2) + 4
18 ­ 10 + 4
8 + 4
12
Assignment
Order or Operations and Substitution Worksheet
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