# Arithmetic properties: Identity property

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##### Intros
###### Lessons
1. Introduction to the identity property of addition and multiplication (and properties of zero):
2. Showing that $a + 0 = a$
3. Why is it called the "identity" property?
4. Showing that a × 1 = a
5. The general formulas for the identity property
6. The three properties of zero involving multiplication and division (a × 0 = 0; 0 ÷ a = 0; and a ÷ 0 = undefined)
7. The general formulas for the properties of zero
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##### Examples
###### Lessons
1. Additive identity property of 0
Use the additive identity of 0 to fill in the blanks.
1. 287 + __ = 287
2. __ + 0 = 0.39
3. 0 + __ = $\large \frac{517}{1000}$
2. Multiplicative identity property of 1
Use the multiplicative identity of 1 to fill in the blanks.
1. 657 × __ = 657
2. 1 × __ = 8.914
3. __ × $\large \frac{832}{900}$ = $\large \frac{832}{900}$
3. Multiplying and dividing using properties of 0
Use the properties of 0 to fill in the blanks.
1. $\large \frac{13}{25}$ × 0 = __
2. __ × 1 = 0
3. 0 ÷ 25 = __
4. 35 ÷ __ = undefined
5. 7.6 × 0 = __
6. 439 ÷ 0 = __
4. Identity properties and all four operations
What happens to the identity of number 46 when:
1. 46 + 0 =
2. 46 - 0 =
3. 46 × 0 =
4. 46 × 1 =
5. 46 ÷ 1 =
6. 46 ÷ 0 =
7. 0 ÷ 46 =
5. Identity properties word problem
If $a$, $b$ and $c$ are real numbers with secret identities:
1. What happens to a when it is added to 0
2. What happens to b when it is multiplied with 1
3. What happens to c when it is multiplied with 0
4. What happens to a when it is divided by 0
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##### Practice
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###### Topic Notes

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

Notes:

• 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 $a × 0 = 0$ $0 × a = 0$ $0 ÷ a = 0$ - - - - - - - - - - - - - - - - - $a ÷ 0 = undefined$