Properties of Addition

Three Properties of Addition

1. Commutative2. Associative3. Zero

The 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.

Commuter A

Commuter B

Commuter ACommuter

B

Commuter A & Commuter B changed lanes.

Remember… commute means to change.

Here is another example…

Think of this hypothetical situation:

Every day you ride your bike to school. The distance from home to school is 2 miles.The distance from school to home is also 2 miles.How do we know this?

Did you notice that hypothetical and hypothesis look almost the same?

Hmmmm... Think about what hypothesis means…

Home School

The distance from Home to School is the same as the distance from school to home.

Home + School = School + Home

H + S = S + HA + B = B + A

The Commutative Property

A + B = B + A

Three Properties of Addition

1. Commutative2. Associative3. Identity

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 do talk to one another.

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.

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)

• 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

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

A C

B

A C

B

THEN THEN

The parentheses identify which two associates talked first.

Three Properties of Addition

1. Commutative2. Associative3. Zero

Zero Property of Addition

A + 0 = A

+ 0 =

Let’s practice !

Look at the problem.

Identify which property it represents.

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

The Associative Property of Addition

It is the only addition property that has parentheses.

12 + 0 = 12

The Identity Property of Addition

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

9 + 7 = 7 + 9

The Commutative Property of Addition

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

4 + 6 = 6 + 4The Commutative Property of Addition

Numbers change places.

3 + 0 = 3 The Zero Property of Addition

See the zero?

(4 + 3) + 2 = 4 + (3 + 2) The Associative Property of Addition

It has parentheses!

a + 0 = a The Zero Property of Addition

Zero!

a + b = b + aThe Commutative Property of Addition

Moving numbers!

A

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

Parentheses!

C

B