Identity property

In this lesson, we will learn:

• What is the additive identity property of zero
• What is the multiplicative identity property of one
• How to write the general formulas/equations for the identity properties
• What are the three properties of zero?
• How the identity properties are different from the properties of zero
• How to write the general formulas/equations for properties of zero

• The identity property is observed when the identity of the original number does NOT change after the equal sign. The answer will be the same number that you started with.
• The numbers can be any real number (whole numbers, fractions, decimals, integers, etc.)
• The word “identity” can mean who you are or what you are



• The identity property only happens for TWO cases in math:
• For addition: adding zero to any number will NOT change that number
• Ex. 8 + 0 = 8
• Ex. 0.5 + 0 = 0.5
• Ex. $\large \frac{1}{2}$ + 0 = $\large \frac{1}{2}$
• For multiplication: multiplying any number by one will NOT change that number
• Ex. 8 × 1 = 8
• Ex. 1.47 × 1 = 1.47
• Ex. $\large \frac{3}{4}$ × 1 = $\large \frac{3}{4}$


• The general formulas for the identity property (where a is $a$ variable that represent a real number) are:



Arithmetic Property	Of Addition	Of Multiplication
(Additive) Identity property of 0	$a + 0 = a$ $0 + a = a$	*
(Multiplicative) Identity property of 1		$a × 1 = a$ $1 × a = a$



• It is important to know the properties of zero – *what happens when you multiply and divide by zero so that you don't get them confused with the identity property of zero
• There are three properties of zero:
• (1) when you multiply by zero, the answer will always be zero
• (2) when zero is divided by any number, the answer will always be zero
• (3) when you attempt to divide any number by zero, the answer will always be undefined


• The general formulas for the properties of zero are:



Arithmetic Property	Of Multiplication	Of Division
Properties of Zero	$a × 0 = 0$ $0 × a = 0$	$0 ÷ a = 0$ - - - - - - - - - - - - - - - - - $a ÷ 0 = undefined$