A negative number is a number below zero, like −7. Picture a number line: adding moves you right, subtracting moves you left, and a negative sign flips the direction.
Try it with your own problem ↓
The steps
- Subtracting a negative is adding a positive. Rewrite a − (−b) as a + b.
- Adding numbers with the same sign: add the sizes and keep the sign. −3 + (−4) = −7.
- Adding numbers with different signs: subtract the smaller size from the bigger one, and keep the sign of the number with the bigger size.
- Multiplying or dividing: multiply or divide the sizes. Same signs give a positive answer, different signs give a negative answer.
A worked example
Work out −7 − (−2).
- Subtracting a negative is the same as adding a positive, so rewrite it as −7 + 2.
- The signs are different. The sizes are 7 and 2; the difference is 7 − 2 = 5.
- The bigger size (7) is negative, so the answer is negative: −5.
- On a number line: start at −7 and move 2 to the right. You land on −5.
−7 − (−2) = −5.
Common mistakes
- Ignoring the second sign. In −7 − (−2), the two minus signs together mean plus.
- Dropping the sign of the bigger number. −9 + 4 is −5, not 5.
- Thinking two negatives always give a negative. They do when adding (−2 + −3 = −5) but not when multiplying (−2 × −3 = 6).
- Mixing up −3² and (−3)². The first is −9. The second is 9.
Questions people ask
Why is a negative times a negative positive?
Think of reversing a reversal. Taking away a debt of $2, three times, leaves you $6 better off: −(−2) × 3 = 6. The sign rules keep all of arithmetic consistent.
Is −5 greater or less than −8?
Greater. On a number line it is farther to the right. Of two negatives, the one closer to zero is larger.
What is the absolute value of −7?
7. It is the distance from zero, so it is never negative.
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