Negative numbers

A negative number is any number that is less than zero. Negative numbers are written with a negative sign (-) in front of them. "-5" is read as negative 5 and has the same magnitude as 5, just in the opposite direction on the number line, as shown in the figure below.

The number line shows that both -5 and 5 have the same magnitude, so -5 + 5 = 0.

The further left on the number line, the more negative the number is, and the smaller the number. The number line extends to negative infinity left of 0, and positive infinity to the right.

Negative numbers are something we are likely to encounter in our daily lives, such as the temperature, so understanding how to perform basic arithmetic using negative numbers can be helpful.

Operations with negative numbers

There are a few rules for how to use negative numbers when performing arithmetic operations.

Addition

Adding a negative number is like subtracting a positive number.

5 + (-3) = 2

We can rewrite the above as:

5 - 3 = 2

The same is true regardless what position the negative number is in:

-3 + 5 = 5 - 3 = 2

When adding two negative numbers, the result is even more negative:

-3 + (-5) = -3 - 5 = -8

Generally, when adding positive and negative numbers, determine which value is larger, then subtract the two values and apply the sign of the larger value.

Subtraction

Subtracting a negative number is like adding a positive number since two negative numbers make a positive number:

5 - (-3) = 5 + 3 = 8

-9 - (-8) = -9 + 8 = -1

Multiplication and division

Multiplication and division follow the same rules regarding negative numbers:

positive × positive = positive

negative × negative = positive

positive × negative = negative

negative × positive = negative

Essentially, an odd number of negatives being multiplied or divided has a negative result. An even number of negatives being multiplied or divided has a positive result:

-3 × -4 ÷ 2 = 6

-3 × 4 ÷ 2 = -6

-3 × (-4) × (-1) ÷ 2 = -6