Opposite Numbers — Definition, Formula & Examples
Opposite numbers are two numbers that sit the same distance from zero on the number line but on opposite sides. For example, 5 and −5 are opposite numbers because they are both 5 units from zero.
For any real number , its opposite is the number such that . The opposite of a number is also called its additive inverse.
Key Formula
Where:
- = Any real number
- = The opposite (additive inverse) of a
How It Works
To find the opposite of any number, simply change its sign. If the number is positive, its opposite is negative; if the number is negative, its opposite is positive. The opposite of zero is zero itself, since . On a number line, you can find the opposite by reflecting the point across zero.
Worked Example
Problem: Find the opposite of −7 and verify your answer.
Change the sign: The opposite of −7 is found by switching its sign from negative to positive.
Verify: Add the two numbers together. If they are opposites, their sum must equal zero.
Answer: The opposite of −7 is 7.
Why It Matters
Opposite numbers appear constantly when solving equations — every time you subtract a term from both sides, you are adding its opposite. Understanding this concept is essential for mastering integer arithmetic and algebra in middle school and beyond.
Common Mistakes
Mistake: Confusing the opposite of a number with its absolute value.
Correction: The opposite of 5 is −5 (different sign, same distance from zero), while the absolute value of −5 is 5 (always nonnegative). Opposite changes the sign; absolute value removes it.