Signed Numbers

Add, subtract, multiply, and divide positives and negatives.

The idea

The signed numbers extend the counting numbers with negatives, which record direction as well as size: money owed rather than held, degrees below zero rather than above. Picture them on a number line, with zero in the middle, the positives to the right, and the negatives to the left.

To add a number, move along the line: right for a positive, left for a negative. Adding two negatives lands further left, and adding numbers of opposite sign moves toward whichever is larger in size. The figure traces one such sum: starting at $a$ and adding a negative number $b$ moves left, landing at $a + b$.

To subtract a number, add its opposite. In particular, $a - (-b) = a + b.$ Having a debt taken away leaves you better off.

Multiplication and division share one rule: matching signs give a positive result, differing signs a negative one. Applied to a power, the rule says a negative base raised to an even power comes out positive — the negative factors pair off — while an odd power leaves one factor unpaired and the result negative.

Ways to work on it

• Walkthrough. Sign rules for each of the four operations.
• Practice. Practice each of the four operations on signed numbers.
• Hardest. Combine operations with signs in PEMDAS order.

Not sure where to start? Take the ten-question placement test.