Negative numbers are numbers less than zero. They appear on the left of zero on a number line.
Ordering: $-5 < -2 < 0 < 3$ — more negative means smaller.
Adding and subtracting:
- Adding a negative: $6 + (-4) = 6 - 4 = 2$
- Subtracting a negative: $3 - (-5) = 3 + 5 = 8$
Multiplying and dividing:
- Same signs → positive: $(-3) \times (-4) = 12$, $(-12) \div (-3) = 4$
- Different signs → negative: $(-3) \times 4 = -12$, $12 \div (-3) = -4$
Powers of negatives: $$(-2)^2 = 4 \quad \text{(even power → positive)}$$ $$(-2)^3 = -8 \quad \text{(odd power → negative)}$$
Note: $-2^2 = -4$ (the square applies to 2 only, not the negative sign).
Common error: confusing $(-2)^2 = 4$ with $-2^2 = -4$ — brackets matter.