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Multiplication Properties

- Lesson 6.5

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

In multiplication, you will see these same

properties, plus 2 more

Five Properties of Multiplication

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

Lets review the addition properties from the

multiplicative perspective

- Multiplicative (Do you see most of the word

multiply in this word?

Property 1

- The Commutative Property
- of Multiplication

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.

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

The Commutative Property

- A B B A

Here is another example

3 groups of 5 5 groups of 3

3 x 5

5 x 3

15 kids

15 kids

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

Property 2

- The Associative Property
- of Multiplication

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.

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?

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?

(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.

The Associative Property

The parentheses identify which two associates

talked first.

(A ? B) ? C A ? (B ? C)

THEN

THEN

Property 3

- The Identity Property
- of Multiplication Property of One

The Identity PropertyProperty of One

I am me! You cannot change My identity!

One is the only number you can multiply something

by and see no change.

Identity Property of MultiplicationProperty of

One

x 1

- a x 1 a

Identity Property of MultiplicationProperty of

One

x 1

x 1

x 1

- a x 1 a

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

There are two more properties which are unique to

multiplication

- The Zero Property
- The Distributive Property

Property 4

- The Zero Property of Multiplication

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!

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

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

Lets practice !

Look at the problem. Identify which property it

represents.

987 1 987

The Identity Property of Multiplication

- Times 1

3 0 0

Zero Property of Multiplication

- Times zero

(1 2) 3 1 (2 3)

The Associative Property of Multiplication

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

6 11 11 6

The Commutative Property of Multiplication

- Same 2 numbers
- Numbers switched places

9 7 7 9

The Commutative Property of Multiplication

- Same 2 numbers
- Numbers switched places

12 0 0

Zero Property of Multiplication

- Times zero

(9 8) 7 9 (8 7)

The Associative Property of Multiplication

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

9 1 9

The Identity Property of Multiplication

- Times 1

a 1 a

The Identity Property of Multiplication

a b b a

The Commutative Property of Multiplication

(a b) c a (b c)

The Associative Property of Multiplication

a 0 0

The Zero Property of Multiplication

(No Transcript)

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