Lesson 3 — Opposite of a Number

🎯 Goal

Learn what it means for numbers to be opposites and how opposites are used in addition and subtraction.

📖 Lesson Description

Every real number has an opposite (also called its additive inverse). The opposite of a number is the same distance from zero on the number line but in the opposite direction.

🔎 Opposites Defined

• The opposite of \(a\) is \(-a\).
• The opposite of \(-a\) is \(a\).
• Zero is its own opposite: \(0 = -0\).

Rule: A number and its opposite always add to zero. \[ a + (-a) = 0 \]

📝 Examples

• The opposite of \(7\) is \(-7\).
• The opposite of \(-12\) is \(12\).
• \(5 + (-5) = 0\)
• \(-8 + 8 = 0\)
• Zero’s opposite is still \(0\).

✏️ Practice

1. What is the opposite of \(15\)?
2. What is the opposite of \(-20\)?
3. Fill in the blank: \(9 + \_\_ = 0\)
4. True or false: The opposite of \(0\) is \(-0\).
5. On a number line, mark \(-6\) and its opposite. How far apart are they?