The properties of real numbers help us simplify math expressions

and help us better understand the concepts of algebra.

Commutative Properties

• Numbers can be added or multiplied in any order.

• a + b = b + a 1 + 3 = 3 + 1• a × b = b × a 2 x 6 = 6 x 2

Why is this important? 15 + 7 + 5 $4. 30 + $10.50 + $0.70 + $0.50 6 x 12 x 5

• Does Commutative Property work with Subtraction?

10 - 5 = 5 - 10

• Does Commutative Property work with Division?

50 ÷ 10 = 10 ÷ 50

Identity Properties

• Identity property of addition - the sum of zero and any number or variable is the number or variable itself.

• When you add 0 to any number, it will always keep its identity!!!!

5 + 0 = 5 A + 0 = A

• Identity property of multiplication - the product of 1 and any number or variable is the number or variable itself.

5 X 1= 5 B x 1 = B

Identity Properties

Associative Properties

• The associative property of addition - when adding more than two numbers the grouping of the numbers does not change the sum.

(a + b) + c = a + (b + c)Example: (29 + 13) + 7 = 29 + (13 + 7)

Notice how adding the 13 + 7 first makes completing the problem easier mentally

• The associative property of multiplication - when multiplying more than two numbers the grouping of the factors does not change the product.

(a x b) x c = a x (b x c)

Example: (6 x 4) x 5 = 6 x (4 x 5)

Notice how multiplying the 4 and 5 first makes completing the problem easier.

Associative Properties

Distributive Properties

• The distributive property lets you multiply a sum by multiplying each number separately and then add the products.

•

• 4 ( 45)= 4 (40) + 4(5)

• 20(13)=