Properties of Real Numbers Commutative Associative Identity Inverse

Properties of Real Numbers Commutative Associative Identity + × Inverse + × Zero Property Reflexive Distributive

Commutative Properties Changing the order of the numbers in addition or multiplication will not change the result. Commutative Property of Addition states: 2 + 3 = 3 + 2 or a + b = b + a. Commutative Property of Multiplication states: 4 • 5 = 5 • 4 or ab = ba.

Verbal Hints for Commutative Property Commute Switch Places Move to a new location

Associative Properties 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 or a + (b + c)= (a + b)+ c Associative Property of Multiplication states: (2 • 3) • 4 = 2 • (3 • 4) or (ab)c = a(bc)

Verbal Hints for Associative Property Regroup They simply group with a new friend ( ) change places but numbers stay the same

Additive Identity Property 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.

Multiplicative Identity Property 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.

Verbal Hints for Identity Property The value that returns the input unchanged Remember “I” in the word identity

Additive Inverse Property 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.

Verbal Hints for Additive Inverse Opposite numbers Same number but different sign Zero Pairs

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

Verbal Hints for Multiplicative Inverse Flip the number Reciprocal

Zero Property of Multiplication Any number multiplied by 0 is equal to 0 A● 0=0 -23 ● 0 = 0 ½● 0=0 0. 25 ● 0 = 0 “zero times any value is 0

Reflexive Property A number is always equal to itself A=A -2 = -2 5=5 A real number is always equal to itself

Distributive Property Multiplication distributes over addition.

Verbal Hints for Distributive Property Multiplication distributes across addition or subtraction. Multiply across the parentheses!!!!!

Let’s play “Name that property!”

State the property or properties that justify the following. 3+2=2+3 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) = 3 x – 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

2. 3+7=7+3 Commutative Property of Addition

3. 8+0=8 Identity Property of Addition

5. 6 • 4=4 • 6 Commutative Property of Multiplication

11. 5 • 1=5 Identity Property of Multiplication

25. 1 5/ + 0 = 7 1 5/ 7 Identity Property of Addition

40. a + (-a) = 0 Inverse Property of Addition

Properties of Real Numbers Commutative Associative Distributive Identity + × Inverse + ×