Multiplication Properties

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Multiplication Properties

• Lesson 6.5

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Do you remember these Properties of Addition?

• Commutative Property of Addition
• The numbers move around
• a b b a
• Associative Property of Addition
• Grouping with parentheses
• (a b) c a (b c)
• Zero (Identity) Property of Addition
• The identity of the problem does not change
• a 0 a

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In multiplication, you will see these same
properties, plus 2 more
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Five Properties of Multiplication

• These are the basically the same as addition
• Commutative
• Associative
• Identity
• These belong to multiplication only
• Zero
• Distributive

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Lets review the addition properties from the
multiplicative perspective

• Multiplicative (Do you see most of the word
  multiply in this word?

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Property 1

• The Commutative Property
• of Multiplication

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The Commutative Property

• Background
• The word commutative comes from the verb to
  commute.
• Definition on dictionary.com
• Commuting means changing, replacing, exchanging,
  switching places, trading places
• People who travel back and forth to work are
  called commuters.

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Here are two families of commuters.
Hi! Remember us?
Commuter B
Commuter A
Commuter A Commuter B changed lanes.
Remember commute means to switch places.
Commuter A
Commuter B
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The Commutative Property

• A B B A

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Here is another example
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3 groups of 5 5 groups of 3
3 x 5
5 x 3



15 kids
15 kids
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What commutative means to multiplication
Remember we said that the word of means
multiply

• 3 groups of 5 5 groups of 3
• 3 5 5 3
• a b b a

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Property 2

• The Associative Property
• of Multiplication

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The Associative Property

• Background
• The word associative comes from the verb to
  associate.
• Definition on dictionary.com
• Associate means connected, joined, or related
• People who work together are called associates.
• They are joined together by business, and they
  have to talk to one another.

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Lets look at another hypothetical situation

• Three people work together.
• Associate B needs to call Associates A and C to
  share some news.
• Does it matter who he calls first?

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Here are three associates.
B calls A first
He calls C last
If he called C first, then called A, would it
have made a difference?
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(The Role of Parentheses)

• In math, we use parentheses to show groups.
• In the order of operations, the numbers and
  operations in parentheses are done first. (PEMDAS)

So.
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The Associative Property
The parentheses identify which two associates
talked first.
(A ? B) ? C A ? (B ? C)
THEN
THEN
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Property 3

• The Identity Property
• of Multiplication Property of One

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The Identity PropertyProperty of One
I am me! You cannot change My identity!
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One is the only number you can multiply something
by and see no change.
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Identity Property of MultiplicationProperty of
One
x 1

• a x 1 a

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Identity Property of MultiplicationProperty of
One
x 1
x 1
x 1

• a x 1 a

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These are 3 of the Properties of Multiplication

• Commutative Property of Multiplication
• The numbers move around
• a b b a
• Associative Property of Multiplication
• Grouping with parentheses
• (a b) c a (b c)
• Identity Property of Multiplication
• The identity of the problem does not change
• a 1 a

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There are two more properties which are unique to
multiplication

• The Zero Property
• The Distributive Property

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Property 4

• The Zero Property of Multiplication

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The Zero Property of Multiplication

• This looks like a mixture of the identity
  property of addition and the identity property of
  multiplication
• Be careful not to mix them up!

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The Zero Property

• Any time you multiply a number by zero, your
  answer is zero!

If I have 2 pockets with NO money in them, then I
have NO money! 2 0 0
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How do I tell the properties apart?

• Commutative
• Numbers switch places
• Associative
• Parentheses on both sides
• Only multiplication on each side
• Identity
• Multiply by 1
• Zero Property
• Multiply by zero

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Lets practice !
Look at the problem. Identify which property it
represents.
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987 1 987
The Identity Property of Multiplication

• Times 1

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3 0 0
Zero Property of Multiplication

• Times zero

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(1 2) 3 1 (2 3)
The Associative Property of Multiplication

• Same 3 numbers
• Multiplication only
• 2 sets of parentheses

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6 11 11 6
The Commutative Property of Multiplication

• Same 2 numbers
• Numbers switched places

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9 7 7 9
The Commutative Property of Multiplication

• Same 2 numbers
• Numbers switched places

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12 0 0
Zero Property of Multiplication

• Times zero

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(9 8) 7 9 (8 7)
The Associative Property of Multiplication

• Same 3 numbers
• Multiplication only
• 2 sets of parentheses

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9 1 9
The Identity Property of Multiplication

• Times 1

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a 1 a
The Identity Property of Multiplication
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a b b a
The Commutative Property of Multiplication
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(a b) c a (b c)
The Associative Property of Multiplication
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a 0 0
The Zero Property of Multiplication
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