Primary mathematics/Negative numbers
Introduction
Negative numbers are numbers less than zero. A convenient way to think of them is as a number owed. For example, if you have negative four apples, that means you owe four apples to someone. A dash is typically used to indicate a negative value. In our case, we would write -4 apples.
Adding negative numbers
To add two negative numbers, just add normally, then make the result negative:
-4 + -3 = -7
When adding one negative number to one positive number, it can be rewritten as a subtraction problem:
4 + -3 = 4 - 3 = 1
It may be necessary to change the order of the two terms to do this:
-3 + 4 = 4 - 3 = 1
Any subtraction problem can also produce a negative value:
-4 + 3 = 3 - 4 = -1
The last problem can be visualized as if you owed 4 apples, then got 3 (which you gave to the person to whom you owed the apples), so you would still owe them 1 apple.
Subtracting negative numbers
Subtracting a negative number is the same as adding the same positive number. In other words, two negatives makes a positive:
4 - -3 = 4 + 3 = 7
Or, if both numbers are negative:
-4 - -3 = -4 + 3 = 3 - 4 = -1
Multiplying negative numbers
Just multiply normally, then apply the following rules:
- If both numbers are negative (or both are positive), the result is positive.
- If only one number is negative, the result is negative.
Thus:
4 × 3 = 12
-4 × -3 = 12
-4 × 3 = -12
4 × -3 = -12
Dividing negative numbers
Just divide normally, then apply the following rules:
- If both numbers are negative (or both are positive), the result is positive.
- If only one number is negative, the result is negative.
Note that these are the same rules as were used for multiplication:
12 / 4 = 3
-12 / -4 = 3
12 / -4 = -3
-12 / 4 = -3
Other notations
Negative numbers are sometimes shown in parenthesis, in red, or with DB (for DeBit) next to them, in the field of accounting (that is, when dealing with money).