PROPERTIES OF REAL NUMBERS

Commutative Property Associative Property Distributive Property Identity Property + x Inverse Property + X

Changing the order of the numbers in addition or multiplication will not change the result.

Commutative Property of Addition states Commutative Property of Multiplication states

1 + 2= __ _ = 5. 4 _ + 9 = = 7. _

Changing the grouping of the numbers in addition or multiplication will not change the result.

Associative Property of Addition states 3 + (4 + 5)= (3 + 4)+ 5 Associative Property of Multiplication states 3 x(4 x 5)= (3 x 4)x 5

3 + (7 + 5) 5 X (11 X 2) 1 + (2 + 7)

Multiplication distributes over addition.

There exists a unique number 0 such that zero preserves identities under addition.

a + 0 = a and 0 + a = a In other words adding zero to a number does not change its value.

There exists a unique number 1 such that the number 1 preserves identities under multiplication.

a ∙ 1 = a and 1 ∙ a = a In other words multiplying a number by 1 does not change the value of the number.

ADDITITIVE IDENTITY PROPERTY MULTIPLICATIVE IDENTITY PROPERTY a + 0 = a 0 + a = a a ∙ 1 = a 1 ∙ a = a

For each real number a there exists a unique real number – a such that their sum is zero. a + (- a ) = 0 In other words opposites add to zero.

For each real number a there exists a unique real number such that their product is 1.

Let’s play “Name that property!”

PROPERTIES OF REAL NUMBERS Commutative Property Associative Property Distributive Property Identity Property + x Inverse Property + X Closure Property

STATE THE PROPERTY OR PROPERTIES THAT JUSTIFY THE FOLLOWING = Commutative Property

STATE THE PROPERTY OR PROPERTIES THAT JUSTIFY THE FOLLOWING. 10(1/10) = 1 Multiplicative Inverse Property

STATE THE PROPERTY OR PROPERTIES THAT JUSTIFY THE FOLLOWING. 3(x – 10) = 3x – 30 Distributive Property

STATE THE PROPERTY OR PROPERTIES THAT JUSTIFY THE FOLLOWING. 3 + (4 + 5) = (3 + 4) + 5 Associative Property

STATE THE PROPERTY OR PROPERTIES THAT JUSTIFY THE FOLLOWING. (5 + 2) + 9 = (2 + 5) + 9 Commutative Property

3 + 7 = Commutative Property of Addition 2.

8 + 0 = 8 Identity Property of Addition 3.

6 4 = 4 6 Commutative Property of Multiplication 5.

17 + (-17) = 0 Inverse Property of Addition 6.

2(5) = 5(2) Commutative Property of Multiplication 7.

(2 + 1) + 4 = 2 + (1 + 4) Associative Property of Addition 1.

even + even = even Closure Property 8.

3(2 + 5) = Distributive Property 9.

6(78) = (67)8 Associative Property of Multiplication 10.

5 1 = 5 Identity Property of Multiplication 11.

PROPERTIES OF REAL NUMBERS Commutative Property Associative Property Distributive Property Identity Property + x Inverse Property + X Closure Property