# 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.

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).