Math Properties Commutative Associative Distributive and Identity Properties

Math Properties Commutative, Associative, Distributive, and Identity Properties

What are properties? • In life, there are rules and laws that tell us what we can and can not do. . . • In math, properties are like those laws or rules they tell us what we can and can not do with sets of numbers

Commute • To commute means to travel from one place to another. • For example, you commute to school in the morning.

Commutative Property • Just like you commute from home to school, a number may commute from one spot to another. • a + b = b + a (The numbers change places. ) • Ex) 2 + 3 = 3 + 2 • Both 2 + 3 and 3 + 2 equal 5. • a · b = b · a • Ex) 3 · 5 = 5 · 3 • Both 3 · 5 and 5 · 3 equal 15.

Associate • An associate is a friend or someone you work with. • For example, the head cheerleader is an associate of the school mascot.

Now imagine the football team played a late game and the cheerleader and mascot forgot to study for the math test. Suddenly the cheerleader associates with someone else.

Associative Property The associative property is when a number associates with a different number. A + (B + C) = (A + B) + C or 2 + (6 + 5) = (2 + 6) + 5

Associative Property • The associative property may be used with addition as seen previously and also with multiplication. • A · (B · C) = (A · B) · C is called the associative property of multiplication.

Identity • Your identity is who you are. • Changing your clothes or getting a new haircut does not change your identity. • Your identity remains the same.

Identity Properties Identity Property of Addition A + 0 = A Identity Property of Multiplication A · 1 = A

Distribute • Distribute means to deliver or pass out • If we distribute food to three boxes, we put food in each of the three boxes

Distributive Property • The A is the food and the boxes are B and C. • We pass out A to each of B and C. • In this case that means that we multiply A by both B and C separately and then add the resulting products.

Now you try these examples. 1) 5(6 + 3) = 5 · 6 + 5 · 3 2) 7(2 + 4) = 7 · 2 + 7 · 4 3) 2(6 -3) = 2 · 6 – 2 · 3

So let’s try a few. . . • Fill in the blank. • 5) 4(2+10) = _______ • 6) 9(12+15) = _______ • 7) _____ = 8 · 10 + 8 · 17 • 8) _____ = 12 · 4 + 12 · 7