12: Order of Operations PEMDAS

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1-2 Order of OperationsPEMDAS
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WHAT YOULL LEARN

• Use the order of operations to evaluate
  expressions.

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KEY CONCEPT

• Order of Operations
• 1. Evaluate expressions inside grouping symbols.
• 2. Do all multiplications and/or divisions from
  left to right.
• 3. Do all additions and/or subtractions from left
  to right.

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• In your notes, summarize the Order of Operations

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EXAMPLES

• Find the value of each expression.

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EXAMPLES

• Find the value of each expression.

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Your Turn

• Find the value of
  each expression.
• a) (2 4 ) 2
• b) 3 ? 5 2 ? 1

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BUILD YOUR VOCABULARY (pages 23)

• In algebra, statements that are true for any
  number are called properties.

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Numbers
Symbols
Property of Equality
If 9 2 11, then 9 2 may be replaced by 11.
If a b, then a may be replace by b.
Substitution
21 21
a a
Reflexive
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Numbers
Symbols
Property of Equality
If 10 4 6, then 4 6 10
If a b, then b a
Symmetric
If 3 5 8 and 8 2(4), then 3 5 2(4)
If ab and bc, then a c
Transitive
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Name the property of equality shown by each
statement.
EXAMPLES
If k 7, then k 3 7 3.

Substitution
Property of Equality
If a 4 9, then 9 1 4.
Symmetric
Property of Equality
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Your Turn

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  Name the property of equality shown by
  each statement

a) If a 2 5 and 5 3 2, then a 2 3
2. b) If x 7, then 10 x 10 7.
Transitive Property of Equality
Substitution Property of Equality
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Numbers
Symbols
Property
45 0 45 0 6 0 0 is the identity
For any number a, a 0 0 a a
Additive Identity
12 ? 1 12 1 ? 5 5 1 is the identity
For any number a a ?1 1 ?a a
Multiplicative Identity
7 ? 0 0 0 ? 23 0
For any number a a ? 0 0 ?a 0
Multiplicative Property of Zero
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Find the value of 25 8 ( 12 11 ) 11.
Identify the property used in each step.
EXAMPLE

25 8 ( 12 11 ) 11
25 8 ( ) 11
( 25 ) 11
( ) 11
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Your Turn

• Find the value of 30 ( 6 4 ) ? 1 5.
  Identify the property used in each step.

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BUILD YOUR VOCABULARY (pages 23)

• To evaluate an express is the find the value of
  an expression by replacing the variables with
  numbers.

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Evaluate x y 8 if x 4 and y 3.
EXAMPLE

x y 8 4 ( 3 ) 8 Replace x with 4
and y with 3.
12 8 Substitution Property
20 Substitution Property
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Your Turn

• Evaluate each
  expression if a 7 and b 1.

a) 10 a b b) ( a 2 ) 4b
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