13: Commutative and Associative Properties

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1-3 Commutative and Associative Properties
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WHAT YOULL LEARN

• Use the commutative and associative properties
  to simplify expressions

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Numbers
Symbols
Key Concepts
5 7 7 5
For any numbers a and b, a b b a.
Commutative Property of Addition
3 ? 10 10 ? 3
For any numbers a and b, a ? b b ? a
Commutative Property of Multiplication
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(No Transcript)
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• In your notes, write an example for each property

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EXAMPLE

• Name the property shown by each statement.
  

Commutative
Property
of
Addition
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EXAMPLE

• Name the property shown by each statement.
  

Associative
Property
of
Multiplication
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Your Turn

• Name the property shown by each statement.
  

Commutative Property of Multiplication
Associative Property of Addition
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BUILD YOUR VOCABULARY (pages 23)

• To simplify an expression, eliminate all
  parentheses first and then multiply or divide and
  add or subtract.
• (note correction from your notes.)

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Simplify the express (4 ? m) ? 9. Identify the
properties used in each step.
EXAMPLE
(4 ? m) ? 9

Comm. Property of (x)
36m
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Your Turn

• Simplify the expression ( 12 z ) 7.
  Identify the properties used in each step.

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BUILD YOUR VOCABULARY (pages 23)

• Whole numbers are the numbers 0, 1, 2, 3, 4, and
  so on.
• A counterexample is an example that shows that
  the statement is not true .

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• Whole numbers are numbers 0, 1, 2, 3, 4,
• When you add whole numbers, the sum is always a
  whole number.
• The same is true with multiplication.

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Closure Property of Whole Numbers

• Words Because the sum or product of two whole
  numbers is also a whole number, the set of whole
  number is closed under addition and
  multiplication.
• Numbers 2 5 7, and 7 is a whole
  number.
• 2 ? 5 10, and 10 is a whole number.
  

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State whether the statement Subtraction of whole
numbers is commutative is true or false. If
false, provide a counterexample.
EXAMPLE

7 5 5 7 Evaluate each expression
separately.
7 5 5 7 7 5 and 5
7
2
-2
We found a counterexample , so the statement is
false .
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Your Turn

• 
  
  State whether the statement Subtraction of
  whole numbers is associative is true or false. If
  false, provide a counterexample.

False sample answer (12 5) ? 12 (5 3)