Negatives and the number line

Arithmetic stays positive; algebra doesn't. The first step into algebra is getting comfortable with negative numbers — and the number line makes them make sense.

The number line

Picture a line with 0 in the middle: positives to the right, negatives to the left. A number's sign tells you which direction from zero, and its size tells you how far. So −5 sits five steps left of zero — further out than −2.

Adding and subtracting

Adding moves you right; subtracting moves you left — wherever you start.

• 3 + (−5): start at 3, move 5 left → −2
• −4 − 3: start at −4, move 3 further left → −7
• −4 + 6: start at −4, move 6 right → +2

The move that trips people up is subtracting a negative — it's the same as adding. 5 − (−3) means "5, then un-subtract 3" → 5 + 3 = 8. Two minus signs in a row cancel out.