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Order of Operations
Order of Operations
The order of operations is a set of instructions for evaluating numeric expressions.
PEMDAS is a mnemonic that helps us remember the order of operations when simplifying a numeric expression.
P = Parenthesis
E = Exponents
M = Multiplication
D = Division
A = Addition
S = Subtraction
1) Any math that is inside a set of parenthesis must be simplified first.
2) Exponents are next to be simplified after parenthesis.
3) Division and Multiplication have equal precedence, this means their order can be switched if necessary.
4) Addition and Subtraction also have equal precedence, their order can also be switched if necessary.
Definitions
Numeric Expression
A mathematical expression containing numbers only.
(This means there are no variables)
PEMDAS
A mnemonic used to remember the order of operations
when simplifying numeric expressions.
Mnemonic
a device such as a pattern of letters, ideas, or associations
that assists in remembering something.
Comment: It is best to follow PEMDAS as is until students have mastered this skill, and then practice switching the order of multiplication and division and verify that they get the same answer as when they don't switch the order. Similarly, students should explore changing the order of addition and subtraction, and verify that their final answers will be the same.
Essential Questions:
1) Why can we switch the order of multiplication with division and get the same result?
2) Why can we switch the order of addition with subtraction and get the same result?
Examples
Examples
Use the order of operations to simplify the following examples.
[1] (7 - 3)2 + 11
[2] 5(6) - 13
[3] -2(1 + 2)3 + 112
[4] -3(7 - 2) + 8(9)
Solutions to Example 1 to 4:
Solutions to Example 1 to 4:
Check Your Understanding
Check Your Understanding
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