Lesson 2 — Identity Numbers

🎯 Goal

Understand the identity properties of addition and multiplication and why identity numbers are important.

📖 Lesson Description

An identity number is a special number that, when used in an operation, leaves the other number unchanged. These identities form the foundation for algebra and problem solving.

🔎 The Identity Numbers

• Additive Identity: The number 0.
  For any number \(a\): \[ a + 0 = a \quad \text{and} \quad 0 + a = a \]
• Multiplicative Identity: The number 1.
  For any number \(a\): \[ a \times 1 = a \quad \text{and} \quad 1 \times a = a \]

📝 Examples

• \(5 + 0 = 5\) → 0 is the additive identity.
• \(-12 + 0 = -12\) → works for negatives too.
• \(7 \times 1 = 7\) → 1 is the multiplicative identity.
• \(0.5 \times 1 = 0.5\) → works for fractions and decimals.

✏️ Practice

1. Fill in the blank: \( 23 + \_ = 23 \)
2. Fill in the blank: \( 1 \times \_ = 19 \)
3. Does \(0\) work as a multiplicative identity? Why or why not?
4. True or false: Every number has both an additive and multiplicative identity.
5. Explain why identity numbers are important in solving equations.