Properties for Real Numbers

Rules that real numbers follow

Identity PropertiesThe Identity Property for Addition tells us that

zero added to any number is the number itself.

Zero is called the "additive identity.”

Example: 5 + 0 = 5

The Identity Property for Multiplication tells us that the number 1 multiplied times any number gives the number itself.

The number 1 is called the "multiplicative identity.”

Example: 12 X 1 = 12

Distributive PropertyThe distributive property comes into play when

an expression involves both addition and multiplication.

A longer name for it is, "the distributive property of multiplication over addition."

It tells us that if a term is multiplied by terms in parenthesis, we need to "distribute" the multiplication over all the terms inside.

Example : 2(5 + 10)

Associative Properties

The Associative Property of Addition tells us that we can group numbers in a sum in any way we want and still get the same answer.

Example: (4+2) + 7 = 4 + (2 + 7)

The Associative Property of Multiplication tells us that we can group numbers in a product in any way we want and still get the same answer.

Example: 2 X (3 X 4) = (2 X 3) X 4

Commutative PropertiesThe Commutative Property of Addition says

that we can add numbers in any order and get the same sum.

Example: 5 + 4 = 4 + 5

The Commutative Property of Multiplication is very similar. It says that we can multiply numbers in any order we want without changing the product.

Example: 3 X 8 X 5 = 5 X 3 X 8

The Real Number System

Real Number System

Real Number SystemNatural Numbers – A natural number is a

number that occurs commonly and obviously in nature. As such, it is a whole, non-negative number. The set of natural numbers, denoted N, can be defined : N = {0, 1, 2, 3, ...}

Whole Numbers – Also called counting numbers including positive integers and zero. Any of the numbers (0, 1, 2, 3, …).

Real Number System (cont.)

Rational – any number that can be expressed as the quotient or fraction p/q of two integers, p and q, with the denominator q not equal to zero. Since q may be equal to 1, every integer is a rational number.

Irrational - is any real number that cannot be expressed as a ratio of integers. Irrational numbers cannot be represented as terminating or repeating decimals.

Real Number System (cont)

Integers – Integers are the set of whole numbers and their opposites. Whole numbers greater than zero are called positive integers. Whole numbers less than zero are called negative integers. The integer zero is neither positive nor negative, and has no sign.