How to Calculate with Negative Numbers

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When you add numbers together, you jump to the right on the real number line. When you subtract, which means you’re using a minus sign, you jump to the left on the real number line. Let’s first see what happens when you subtract a positive number from a negative number. In that case, you start on a negative number and jump further to the left.

Example 1

You need to subtract $4$ from $- 3$ . You can see in the figure below that we start with the number $- 3$ . Then we jump four numbers to the left on the real line:

A section of the number line from minus nine to minus one

This gives you $- 3 - 4 = - 7$ .

Example 2

You need to subtract

10

from

- 5

. You can see in the figure below that we start with the number

- 5

. Then we jump ten numbers to the left on the real line:

A section of the number line from minus seventeen to minus three

This gives you $- 5 - 10 = - 15$ .

Next, we’ll look at what happens when you subtract a positive number from another positive number, but the number we’re subtracting is greater than the number we’re subtracting it from. In these cases the answer will end up being a negative number. This is because the number of jumps from the starting point to

0

is less than the total number of jumps you need to make. It will look like this:

Example 3

You need to subtract $8$ from $2$ . On the real line below, you can see that we start on $2$ and jump $8$ numbers to the left:

A section of the number line from minus eight to plus three

For that reason, $2 - 8 = - 6$ .

Think About This

What do we need negative numbers for? It might seem weird to do calculations with negative numbers. When do we actually use them in day-to-day life?

Measuring temperature is an example from day-to-day life where we use negative numbers. Look at Example 1 above. The calculation you did there might as well have been an exercise about temperature: Somewhere in Norway the temperature is

- 3

°C right now. You know that it will be

4

°C colder the next day. What will the temperature be the next day?

The next day, the temperature will be $- 3 °C - 4 °C = - 7 °C$ . This means that $- 7 °C$ is $4 °C$ colder than $- 3 °C$ .

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