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 were negative (or both are positive), the result is positive.

• If only one number was 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).