What are opposite numbers?

What are opposite numbers, and what can we do with them?

When we talk about the “opposite of a number,” we’re specifically talking about the positive and negative versions of the same number.

Now that’s not a technical definition by any means, so let me show you what I mean.

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But before we get into that, let’s take a step back and talk about negative numbers. The easiest way to illustrate a negative number is by using the number line.

On this number line, we can see the number $0$ in the center. The numbers to the right of $0$ are always positive numbers; the numbers to the left of $0$ are always negative numbers, and this is always true when we’re talking about a number line like this.

The other important thing to realize about this number line is that the numbers $1$ and $-1$ are the same distance away from $0$. We could say they’re both “one unit” away from $0$, in fact. In the same way, $4$ and $-4$ are the same distance from $0$; they’re both “four units” away from $0$.

And this brings us back to the concept of “opposite” numbers. Opposite numbers are numbers which are the same distance away from $0$. And that’s why $1$ and $-1$ are opposites (because they are the same distance from $0$), and why $4$ and $-4$ are opposites (because they are also the same distance from $0$).

On the other hand, $2$ and $4$ are not opposites of each other, because the number $2$ is two units away from $0$, whereas the number $4$ is four units away from $0$. Two numbers are not opposites of each other if they are different distances away from $0$.

The easiest way to remember how to find the opposite of a number is to add a negative sign if the number is positive, or to take away the negative sign if the number is negative.

Opposite numbers graphed on a number line

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Finding the opposite of a positive number

Example

What is the opposite of $7$?

To find the opposite of the positive number $7$, we simply add a negative sign to get $-7$. Both $7$ and $-7$ are seven units from $0$ on the number line, so $7$ and $-7$ are opposites of each other.

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Let’s try an example with a negative number.

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Opposite numbers are numbers which are the same distance away from 0.

Example

What is the opposite of $-10$?

To find the opposite of the negative number $-10$, we simply take away the negative sign to get $10$. Both $10$ and $-10$ are ten units from $0$ on the number line, so $10$ and $-10$ are opposites of each other.

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How about $0$? Does $0$ have an opposite? We know from looking at the number line from earlier

that we can find the opposite of a number by measuring out the same distance from $0$, but just on the opposite side of $0$. So since $5$ is five units away from $0$ to the right of $0$, then the opposite of $5$ is the number that’s five units away from $0$ to the left of $0$, which is $-5$.

But $0$ itself is “zero units” away from $0$ (keep in mind that it’s the ONLY number that’s “zero units” away from $0$). $0$ isn’t a positive number or a negative number. So the opposite of $0$ is actually $0$. In other words, $0$ is its own opposite!

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