Identity Property of Whole Numbers With Examples

The Identity Property of Whole Numbers is a fundamental concept in mathematics, particularly in arithmetic. This property comes in two forms:

The Identity Property of Addition and the Identity Property of Multiplication.

Let’s explore each in detail with examples.

1. Identity Property of Addition

Definition: The Identity Property of Addition states that when you add zero to any whole number, the sum is the number itself. Zero is called the “additive identity” because it does not change the value of the number it is added to.

Mathematical Representation:

a+0=a

Examples:

• If a = 5, then 5 + 0 = 5.
• If a = 123, then 123 + 0 = 123.
• If a = 0, then 0 + 0 = 0.

2. Identity Property of Multiplication

Definition: The Identity Property of Multiplication states that when you multiply any whole number by one, the product is the number itself. One is called the “multiplicative identity” because it does not change the value of the number it is multiplied by.

Mathematical Representation:

a × 1 = a

Examples:

• If a = 7, then 7 × 1 = 7.
• If a = 50, then 50 × 1 = 50.
• If a = 1, then 1 × 1 = 1.

Understanding Through Real-life Analogies

Addition Example: Imagine you have 8 apples. If you add zero apples to your collection, you still have 8 apples. Nothing has changed because adding zero means you haven’t added any new apples.

Multiplication Example: Imagine you have one bag containing 12 candies. If you have one such bag, you still have 12 candies. Multiplying by one means you have the same number of candies as in one bag.

Visual Representation

Addition:

5 + 0 = 5

Think of 5 stars: ⭐ ⭐ ⭐ ⭐ ⭐ + 0 stars = ⭐ ⭐ ⭐ ⭐ ⭐

Multiplication:

6 × 1 = 6

Think of 6 circles:

⚪ ⚪ ⚪ ⚪ ⚪ ⚪ × 1 = ⚪ ⚪ ⚪ ⚪ ⚪ ⚪

Practice Problems

1. What is 34 + 0?
   • 34 + 0 = 34
2. What is 0 + 89?
   • 0 + 89 = 89
3. What is 15 × 1?
   • 15 × 1 = 15
4. What is 1 × 92?
   • 1 × 92 = 92

Understanding the Identity Property of Whole Numbers helps build a strong foundation in arithmetic, making it easier to grasp more complex mathematical concepts in the future.