Properties of Real Numbers

Reciprocals 2 numbers whose product is 1 are reciprocals of each other.

Absolute Value The absolute value of a number is its distance from 0 on the number line. The absolute value of x is written Examples of absolute value:

Inverse Property Of Multiplication States that reciprocals multiply to 1.

Inverse Property of Addition States that opposites add to zero. 7 + (-7) = 0 and -4 + 4 = 0

Inverse Properties of the Operations Addition is the inverse of subtraction. Subtraction is the inverse of addition. Division is the inverse of multiplication. Multiplication is the inverse of division.

Commutative Property of Addition a + b = b + a When adding two numbers, the order of the numbers does not matter. Examples: 2 + 3 = 3 + 2 (-5) + 4 = 4 + (-5)

Commutative Property of Multiplication a  b = b  a When multiplying two numbers, the order of the numbers does not matter. Examples: 2  3 = 3  2 (-3)  24 = 24  (-3)

Associative Property of Addition a + (b + c) = (a + b) + c When 3 numbers are added, it makes no difference which 2 numbers are added 1st. Examples: 2 + (3 + 5) = (2 + 3) + 5 (4 + 2) + 6 = 4 + (2 + 6)

Associative Property of Multiplication a(bc) = (ab)c When 3 numbers are multiplied, it makes no difference which 2 numbers are multiplied 1st. Examples: 2  (3  5) = (2  3)  5 (4  2)  6 = 4  (2  6)

Distributive Property a(b + c) = ab + ac Multiplication distributes over addition. Examples of the Distributive Property 2 (3 + 5) = (2  3) + (2  5) (4 + 2)  6 = (4  6) + (2  6)

Identity Property of Addition If 0 is added to a number, the result is that number. Example: 3 + 0 = 0 + 3 = 3

Identity Property of Multiplication If a number is multiplied by 1, the result is that number. Example: 5  1 = 1  5 = 5

Identify which property that justifies each of the following. 4  (8  2) = (4  8)  2

Identify which property that justifies each of the following. 4  (8  2) = (4  8)  2 Associative Property of Multiplication

Which Property?? 6 + 8 = 8 + 6

Commutative Property of Addition 6 + 8 = 8 + 6 Commutative Property of Addition

Which Property?? 12 + 0 = 12

Additive Identity Property 12 + 0 = 12 Additive Identity Property

Which Property? 5(2 + 9) = (5  2) + (5  9)

Distributive Property 5(2 + 9) = (5  2) + (5  9) Distributive Property

Which Property? 5 + (2 + 8) = (5 + 2) + 8

Associative Property of Addition 5 + (2 + 8) = (5 + 2) + 8 Associative Property of Addition

Identify which property that justifies each of the following.

Identify which property that justifies each of the following. Multiplicative Inverse Property

Which Property? 5  24 = 24  5

Commutative Property of Multiplication 5  24 = 24  5 Commutative Property of Multiplication

Which Property?? 18 + -18 = 0

Additive Inverse Property 18 + -18 = 0 Additive Inverse Property

-34 1 = -34

Multiplicative Identity Property -34 1 = -34 Multiplicative Identity Property