Multiplication Properties

Multiplication Properties

Lesson 2-1

Do you remember these Properties of Addition?

Commutative Property of AdditionThe numbers move around

a + b = b + a

Associative Property of AdditionGrouping with parentheses

(a + b) + c = a + (b + c)

Identity Property of AdditionThe 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 additionCommutative

Associative

Identity

These belong to multiplication onlyZero

Distributive

Let’s 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 PropertyThe Commutative Property

BackgroundThe word commutative comes from the verb “to commute.”

Definition on dictionary.comCommuting 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.Here are two families of commuters.

Commuter A

Commuter B

Commuter A

Commuter B

Commuter A & Commuter B changed lanes.

Remember… commute means to switch places.

Hi!Remember

us?

The Commutative PropertyThe Commutative Property

A • B = B • AA • B = B • A

Here is another example…

3 groups of 5 = 5 groups of 3

=

15 kids =15 kids

3 x 5 5 x 3=

What commutative means to multiplication…

3 groups of 5 = 5 groups of 3

3 • 5 = 5 • 3

a • b = b • a

Remember… in Lesson 1-11 we said

that the word “of” means multiply

Property #2

The Associative Property

of Multiplication

The Associative PropertyThe Associative Property

BackgroundThe 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.

Let’s look at another hypothetical situation

Let’s 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?

A C

B

Here are three associates. 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?

NO!

(The Role of Parentheses)(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….So….

The Associative PropertyThe Associative Property

(A B) C = A (B C)(A B) C = A (B C)

A C

B

A C

B

THEN THEN

The parentheses identify which two associates talked first.

Property #3

The Identity Property

of Multiplication

The Identity PropertyThe Identity PropertyI am me!

You cannot changeMy identity!

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 MultiplicationIdentity Property of Multiplication

a x 1 = a

x 1 =

Identity Property of MultiplicationIdentity Property of Multiplication

a x 1 = a

x 1 =

x 1 =

x 1 =

These are 3 of the Properties of Multiplication

Commutative Property of MultiplicationThe numbers move around

a • b = b • a

Associative Property of MultiplicationGrouping with parentheses

(a • b) • c = a • (b • c)

Identity Property of MultiplicationThe 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

The End

Property #5

The Distributive Property

of Multiplication

The Distributive PropertyThe Distributive Property

BackgroundThe word distributive comes from the verb “to distribute.”

Definition on dictionary.comDistributing refers to passing things out or delivering things to people

The Distributive Property

a(b + c) = (a • b) + (a • c)A times the sum of b and c = a times b plus a times c

Let’s plug in some numbers first.

Remember that to distribute means delivering items, or handing them out.

Here is how this property works:

5(2 + 3) = (5 • 2) + (5 • 3)

5(2 + 3) = (5 • 2) + (5 • 3)

You went to two houses on one street and three houses on a different street.

Every family bought 5 items!

You went to two houses on one street and three houses on a different street. Every family bought 5

items!

You have sold many items for the RCMS fundraiser!

You will be distributing 5 items to each house.

1

23

4

5

5(2 + 3) = (5 • 2) + (5 • 3)

You distributed (delivered) these all in one trip.

There are (2+3) five houses all together.

You need to deliver 5 gifts to each house.

You need to put 25 items on your wagon at one time.

5 items x 5 houses = 25 items all together

5(2 + 3) = (5 • 2) + (5 • 3)

You distributed your items in two trips (+).

On the first trip you distributed 5 items to each of 2 houses (5 x 2 = 10).

On the second trip you distributed 5 items to each of 3 houses (5 x 3 = 15).

That means you distributed (delivered) 10 items plus 15 items. That makes 25 items altogether.

and

10

15+

25

The Distributive Property

DISTRIBUTION CENTER

Make 1 trip. You have 5 houses. You need to bring 5 items to each house. You need 25 items on your wagon.

5(2 + 3)

The Distributive Property

DISTRIBUTION CENTER

Make 2 trips. You have 2 houses for your first trip and you need to bring 5 items to each house. You have 3 houses on your second trip and need to bring 5 items to each house. When your second trip is over, you will have distributed 25 items.

(5 • 2) + (5 • 3)

How do I tell the properties apart?

CommutativeNumbers switch places

AssociativeParentheses on both sidesOnly multiplication on each side

IdentityMultiply by 1

Zero PropertyMultiply by zero

DistributiveParentheses on each sideOne side has a multiplication sign AND a plus sign

Let’s practice !Let’s practice !

Look at the problem.

Identify which property it represents.

4(5 + 6) = (4 • 5) + (4 • 6)

The Distributive Property

of Multiplication

•3 numbers on one side—4 on the other

•Multiplication AND addition

•3 sets of parentheses

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(8 + 7) = (9 • 8) + (9 • 7)

The Distributive Property

of Multiplication

•3 numbers on one side—4 on the other

•Multiplication AND addition

•3 sets of parentheses

9 • 1 = 9

The Identity Property

of Multiplication

•Times 1

a • 1 = a The Identity Property

of Multiplication

a • b = b • aThe Commutative Property

of Multiplication

A

(a + b) + c = a + (b + c) The Associative Property

of Multiplication

C

B

a • 0 = 0 The Zero Property

of Multiplication

a(b • c) = (a • b) + (a • c)

The Distributive Property

of Multiplication