Properties of Addition

Properties of Addition

To identify addition propertiesTo identify addition properties

MENTAL MATH• Tell me which is greater.

• 1. 2 + 1 or 2 + 2 ______________

• 2. 5 + 3 or 5 – 2 ______________

• 3. 6 – 1 or 6 – 2 ______________

• 4. 4 – 2 or 4 – 1 ______________

• 5. 10 – 1 or 8 + 1 ______________

Three Properties of AdditionThree Properties of Addition

Addition properties are like

special tools.

They make it easier to work with

numbers.

The Commutative PropertyThe Commutative Property

• Background– The word commutative comes from the

verb “to commute.”– Definition on dictionary.com

• Commuting means changing, replacing, or exchanging

– People who travel back and forth to work are called commuters.• Traffic Reports given during rush hours are

also called commuter reports.

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 change.

Here is another example…

Commutative Property

You can add in any order.

5 + 2 = 7 * 2 + 5 = 7

3 + 6 + 7 = 16 * 7 + 3 + 6 = 16

The Associative PropertyThe 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 do 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.

So….So….

Associative Property

You can change the grouping.

REMEMBER: Add the numbers in parentheses first.

* (6 + 3) + 5 = 14 * 6 + (3 + 5) = 14

* (8 + 2) + 4 = 14 * 8 + (2 + 4) = 14

The Identity Property of AdditionThe Identity Property of AdditionI am me!

You cannot changeMy identity!

I am me!You cannot change

My identity!

Zero is the only number you can add to something

and doesn’t change.

Identity Property of AdditionIdentity Property of Addition

A + 0 = A

+ 0 =

Let’s practice !Let’s practice !

Look at the problem.

Identify which property it represents.

(9 + 8) + 7 = 9 + (8 + 7)

It is the only addition property that has parentheses.

12 + 0 = 12

It is the only addition property that has two addends and one of them is a zero.

9 + 7 = 7 + 9

It is the only addition property that has numbers that change places.

4 + 6 = 6 + 4

Numbers change places.

3 + 0 = 3

See the zero?

(4 + 3) + 2 = 4 + (3 + 2)

It has parentheses!

a + 0 = a

Zero!

a + b = b + a

Moving numbers!

A

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

Parentheses!

C

B