 # How to Calculate with Negative Numbers

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

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 $-3\phantom{\rule{0.17em}{0ex}}\text{°C}-4\phantom{\rule{0.17em}{0ex}}\text{°C}=-7\phantom{\rule{0.17em}{0ex}}\text{°C}$. This means that $-7$ °C is $4$ °C colder than $-3$ °C.

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