Commutative and Associative Properties

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Commutative and Associative Properties
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Properties of Addition and Multiplication
These properties are the rules of the
road. They let us know if a particular maneuver
is legal or not. There are not very many of
them, but you need to memorize them so that you
will know what you can, and cant, do when you
add, subtract, multiply and divide.
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Commutative Property of Addition
When you commute you go Home
Work then Work Home The
commutative property of addition follows the same
pattern a b b a
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Commutative Property of Addition
a b b a Using numbers 3 5 5 3
8 8
Same answer! Order does not matter when we
add. Addition is commutative
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Commutative Property of Subtraction?
Seems obvious, but what about subtraction? Does
order matter when you subtract?

Different answers! YES order does matter when
you subtract! Subtraction is not commutative
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Commutative Property of Multiplication
How about multiplication? Does order matter when
you multiply?
Same answer!
NO order
does NOT matter when you multiply! Multiplication
is commutative
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Commutative Property of Division?
What about division? Does order matter when you
divide?
Different answers! YES order
does matter when you divide! Division is not
commutative
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Associative Property of Addition
Frequently the group of people who live in a
neighborhood form a neighborhood
association. In math, a grouping symbol is the
parentheses ( ). The associative property of
addition tells us that we can group our numbers
any way we want to and still get the same
answer. ( a b ) c a ( b c )
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Associative Property of Addition
( a b ) c a ( b c ) Using numbers ( 2
3 ) 7 2 ( 3 7 )
5 7 2 10
12 12
Same answer! Addition is associative
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Associative Property of Multiplication
( a . b ) . c a . ( b . c ) Using numbers


Same answer! Addition is
associative
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Associative Property

• Just like the commutative property,
• the associative property does work with
• addition
• multiplication
• the associative property does not work with
• Subtraction
• division.

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Associative vs. Commutative
Some people have difficulty keeping these two
properties straight. If the numbers move (change
order) 2 3 3 2 its the commutative
property. If the numbers stand still and the
parentheses move ( 2 3 ) 7 2 ( 3 7
) its the associative property.
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Trick question
Which property is illustrated by the
following 7( 2 3 ) 7( 3 2) As soon as
some people see the parentheses, they say
associative - but the parentheses didnt
move. What changed was the order of the 2 and the
3. It is the commutative property of addition.
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Commutative and Associative Properties

• The commutative properties of addition and
  multiplication involve the order in which the
  numbers are written the numbers move.
• The associative properties of addition and
  multiplication involve grouping the parentheses
  move.
• These properties do not work with subtraction or
  division.