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The basic Number Properties (or laws) that apply to arithmetic operations are Commutative Property, Associative Property, Identity Property and Distributive Property.

The following table gives the commutative property, associative property and identity property for addition and subtraction. Scroll down the page for more examples and solutions of the number properties.

## Identity Properties

### Identity Property (or Zero Property) of Addition

### Identity Property (or One Property) of Multiplication

### Zero Property of Multiplication

**Identity Property of Addition & Multiplication**

Identity Property of Addition: Any number plus zero is the original number.

Identity Property of Multiplication: Any number times one is the original number.

Zero is the identity number of addition and one is the identity number of multiplication.

**Commutative, Associative, and Identity Properties**

Example:

1. Tell which property is represented

a) (2 ˙ 6) ˙ 1 = 2 ˙ (6 ˙ 1)

b) 3 + 0 = 3

c) 7 + 9 = 9 + 7

2. Simplify each expression. Justify each step.

a) 17 + 14 + 3

b) 12 ˙ 3 ˙ 5

c) 21 + 16 + 9

**Identity Property of Addition and Multiplication**

Identity Property of addition states that any number plus zero is the original number.

Identity property of multiplication states any number times one is the original number.

**Identity Property**

This video defines the Identity Property.

The Identity Property is made up of two parts: Additive Identity and Multiplicative Identity.

The Additive Identity is

Add zero (0) to a number, the sum is that number.

The Multiplicative Identity is

Multiply a number by 1, the Product is that number.

Divide a number by itself, the Quotient is 1.

**What is the identity property?**

How can you recognize it and name it when you see it?

Why does it have the name it has?

Why do mathematicians give everything, even something as seemingly simple as this a name?**Commutative & zero properties of multiplication**

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

More Lessons on Numbers

Integer Worksheets

Integer Games

The following table gives the commutative property, associative property and identity property for addition and subtraction. Scroll down the page for more examples and solutions of the number properties.

When you add 0 to any number, the sum is that number.

For example: 325 + 0 = 325.

When you multiply any number by 1, the product is that number.

For example: 65, 148 × 1 = 65, 148

The product of any number and 0 is 0

For example: 874 × 0 = 0

Identity Property of Addition: Any number plus zero is the original number.

Identity Property of Multiplication: Any number times one is the original number.

Zero is the identity number of addition and one is the identity number of multiplication.

Example:

1. Tell which property is represented

a) (2 ˙ 6) ˙ 1 = 2 ˙ (6 ˙ 1)

b) 3 + 0 = 3

c) 7 + 9 = 9 + 7

2. Simplify each expression. Justify each step.

a) 17 + 14 + 3

b) 12 ˙ 3 ˙ 5

c) 21 + 16 + 9

Identity Property of addition states that any number plus zero is the original number.

Identity property of multiplication states any number times one is the original number.

This video defines the Identity Property.

The Identity Property is made up of two parts: Additive Identity and Multiplicative Identity.

The Additive Identity is

Add zero (0) to a number, the sum is that number.

The Multiplicative Identity is

Multiply a number by 1, the Product is that number.

Divide a number by itself, the Quotient is 1.

How can you recognize it and name it when you see it?

Why does it have the name it has?

Why do mathematicians give everything, even something as seemingly simple as this a name?

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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