Adding and Subtracting Negative Numbers

Negative numbers have a minus sign in front and sit to the left of zero on the number line: −1, −2, −3 and so on. A number with no sign is positive. Zero is neutral, neither negative nor positive; it is the boundary between the two. Temperatures below freezing, such as −7°C, are everyday negative numbers.

Use a number line: adding moves right, subtracting moves left. For −7 + 5, start at −7 and move 5 to the right: −2. For −6 − 3, start at −6 and move 3 to the left: −9. If the temperature is 3°C and drops by 10°C, that is 3 − 10 = −7°C. When two signs sit together, use the rules in question 3.

The two minus signs become a plus. Same signs together make a plus, different signs make a minus: 5 − (−3) is 5 + 3 = 8, and 5 + (+3) is also 5 + 3. On the number line, subtracting a negative moves you to the right. With two negatives, −7 − (−4) becomes −7 + 4 = −3.

No. Adding a negative number moves you further left, so two negatives added together make a bigger negative: −12 + (−8) is −12 − 8 = −20, because the different signs next to each other become a minus. It is only subtracting a negative that turns into a plus. Think of two debts: owing £12 and then another £8 means owing £20.

Flip the sign of every term inside, then drop the brackets. For −12 − (−12 + 5): minus −12 becomes +12 and minus +5 becomes −5, so it is −12 + 12 − 5 = −5. Or work out the bracket first: −12 + 5 = −7, then −12 − (−7) = −12 + 7 = −5. Both ways agree, so use one to check the other.

Temperature: 3°C that drops by 10°C is 3 − 10 = −7°C. Money: owing £20 is −20, and paying back £8 is −20 + 8 = −12, so you still owe £12. Depth: a submarine at −120 m that rises 50 m and then dives 30 m is at −120 + 50 − 30 = −100 m. The number line works the same in every case.