Numbers don't stop at zero. When the temperature drops below freezing, or you owe money, you need numbers less than zero — negative numbers. Together with zero and the counting numbers, they make up the integers. This lesson shows what negative numbers mean and how to add and subtract with them using the number line.
The integers are the whole numbers and their negatives: … −3, −2, −1, 0, 1, 2, 3 … A negative number is less than zero, written with a minus sign in front, like −2. On the number line, positive numbers go right of zero and negative numbers go left of zero.
Negative numbers are real and useful: a temperature of −5°C is 5 degrees below freezing, and a balance of −$10 means you owe $10. The further left on the line, the smaller the number, so −5 is smaller than −2.
The number line makes adding and subtracting integers easy: adding moves you right, and subtracting moves you left. Start at the first number and step the right way. For −2 + 5, start at −2 and move 5 steps right, landing on 3.
For 3 − 5, start at 3 and move 5 steps left, passing zero and landing on −2. Whenever you subtract more than you have, you cross zero into the negatives.
Every number has an opposite the same distance from zero on the other side: the opposite of 4 is −4. Adding a number and its opposite gives zero (4 + (−4) = 0).
One rule to remember: subtracting a negative is the same as adding. Taking away a debt is like gaining money, so 5 − (−3) = 5 + 3 = 8. Two minus signs together turn into a plus.
Try these. Pick an answer to see whether it's right and why.