Properties of Addition

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 B Commuter A Commuter A & Commuter B changed lanes. Remember… commute means to change. Commuter A Commuter B

Think of this situation: If 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?

Home + School = School + Home The distance from Home to School is the same as the distance from school to home. Home + School = School + Home H + S = S + H A + B = B + A

The Commutative Property A + B = B + A

Commutative Property of Addition changing the order in which you add does not change the sum

The Identity Property of Addition I am me! You cannot change My identity!

Zero is the only number you can add to something and see no change.

Identity Property of Addition + 0 = A + 0 = A

Identity Property Identity Property of Addition--if you add zero to a number, you get the same number! 0 is called the identity of addition!!

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 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 B calls A first He calls C last A C 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. So….

The Associative Property The parentheses identify which two associates talked first. (A + B) + C = A + (B + C) B B A C THEN A THEN C

Associative Property Associative Property of Addition--changing the way the numbers are grouped does not change the sum.

Let’s practice ! Look at the problem. Identify which property it represents.

The Associative Property of Addition (9 + 8) + 7 = 9 + (8 + 7) The Associative Property of Addition It is the only addition property that has parentheses.

The Identity Property of Addition 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.

The Commutative Property of Addition 9 + 7 = 7 + 9 The Commutative Property of Addition It is the only addition property that has numbers that change places.

The Commutative Property of Addition 4 + 6 = 6 + 4 The Commutative Property of Addition Numbers change places.

The Identity Property of Addition 3 + 0 = 3 The Identity Property of Addition See the zero?

The Associative Property of Addition (4 + 3) + 2 = 4 + (3 + 2) The Associative Property of Addition It has parentheses!

The Identity Property of Addition a + 0 = a The Identity Property of Addition Zero!

The Commutative Property of Addition a + b = b + a The Commutative Property of Addition Moving numbers!

The Associative Property of Addition (a + b) + c = a + (b + c) The Associative Property of Addition Parentheses! B A C

Properties of Multiplication

Commutative Property Commutative Property of Multiplication--changing the order in which you multiply numbers doesn’t change the product.

Associative Property Associative Property of Multiplication--changing the way the numbers are grouped does not change the product.

Identity Property Identity Property of Multiplication--if you multiply a number by 1, you get the same number! 1 is called the identity of multiplication!!

Zero Property (of Multiplication) Any number multiplied by 0 equals 0!