Lesson 03: Identity Numbers

Page Menu

• Lesson Description
• Learning Objectives
• Topics Covered
• Key Terms
• Lesson Examples
• Practice Problems
• Tips & Common Mistakes
• Summary
• Challenge Problems
• Unit Navigation

Lesson Description

This lesson introduces identity numbers—numbers that do not change other numbers under addition or multiplication—and explains their importance in arithmetic operations.

Learning Objectives

• Understand what additive and multiplicative identity numbers are.
• Apply identity numbers in arithmetic operations correctly.
• Recognize the role of identity numbers in simplifying algebraic expressions.

Topics Covered

• Additive Identity (0)
• Multiplicative Identity (1)
• Using identity numbers in calculations

Key Terms

• Additive Identity: A number that, when added to any number, leaves it unchanged (0).
• Multiplicative Identity: A number that, when multiplied by any number, leaves it unchanged (1).
• Identity Property: The property that describes the effect of identity numbers in arithmetic.

Lesson Examples

Example 1: Additive Identity

1. Take the number 7.
2. Add 0 to it: 7 + 0.
3. Observe that the result is still 7. Hence, 0 is the additive identity.

Example 2: Multiplicative Identity

1. Take the number 9.
2. Multiply it by 1: 9 × 1.
3. Observe that the result is still 9. Hence, 1 is the multiplicative identity.

Practice Problems

1. Use the additive identity to simplify: 12 + 0.
2. Use the multiplicative identity to simplify: 15 × 1.
3. Identify the additive and multiplicative identities in the following equations: 0 + x, 1 × y.
4. Apply identity numbers to simplify: 0 + 23 × 1.

Tips & Common Mistakes

• Remember that 0 does not change numbers when added.
• Remember that 1 does not change numbers when multiplied.
• Do not confuse the two identities: 0 is additive, 1 is multiplicative.

Summary

Identity numbers are essential in arithmetic and algebra. The additive identity (0) keeps numbers unchanged under addition, and the multiplicative identity (1) keeps numbers unchanged under multiplication. Understanding these helps simplify calculations and solve problems efficiently.

Challenge Problems

1. Identify the identity numbers in the expression: (x × 1) + 0.
2. Simplify: 0 + (5 × 1) + 0.
3. Create a real-world scenario where using identity numbers simplifies calculations.