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Associative Property

• Keep the same order, just move the parenthesis.(a + b) + c = a + (b + c)(ab)c = a(bc)

Commutative Property

When you add or multiply two numbers, you will get the same answer when you switch the order.a + b = b + aab = ba

Identity PropertyThe number you can

add or multiply by and still get the same number.

a + 0 = a

a · 1 = a

Inverse PropertyWhat number can you add to a and get 0?

a + (-a) = 0

What number can you multiply a by and get 1?a(1/a) = 1

Zero Product Property

The Zero Product Property states that if you multiply two numbers and get zero, then one or both of the numbers MUST be zero.1. 7•0 = 02. (x + 3)(x – 4) = 0 means either x + 3 =

0 or x – 4 = 0 or they both equal zero

Transitive Property• If A = B and B = C, then A = C

• For example:5 + 3 = 4 + 4

• 4 + 4 = 2 + 6• Therefore, 5 + 3 = 2 + 6

• Another example: 7x + 4 = 8b – 8

• 8b – 8 = 56 – y• Therefore,

7x + 4 = 56 –y

Reflexive Property• By now you should have picked out your home,

figured out your commute, created your home identity and examined your square footage.

• It’s time to Buy. • If you buy HOUSE A, then you will end up with

HOUSE A.• The reflexive property states equivalence.• House A = House A, 7 = 7, 112 = 112

Distributive Property• This property “distributes” a value to each

number in the parenthesis.a(b + c) = ab + ac

Everyone in this problem got an “a”

• If you are the mortgage company and folks don’t pay their mortgage, you take back this home, and that home, and the other home.ab + ac = a(b+c)

The Properties of Algebra

• Associative Property• Commutative Property• Identity Property• Inverse Property• Zero Product Property• Transitive Property• Reflexive Property• Distributive Property