Properties of Addition The Commutative Property Background The

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

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 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 m e ! You c annot chang e My ide ntity!

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 calls A first He calls C last B A If he called C first, then called A, would it have made a difference? NO! C

(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 THEN A 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.

(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+4 The Commutative Property of Addition Numbers change places.

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

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

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

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

(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!