Negatives on the Number Line — Visualization & Examples

(Video) Negative Numbers

by Math Antics

Here is a Youtube video by Math Antics that covers Negative Numbers on a Number Line.

$\large{\text{Summary}}$

Negative numbers are on the left side of $0$ on the number line. The negative numbers are a mirrored image of the numbers on the right side of $0$ on the number line (positive numbers). Hence this portion of the number line is called the negative number line.

$0$ is the special number that separates the positive numbers from the negative numbers.

When you start from $0$ on the number line and move to the right, the numbers get larger as you move along. We label all of the natural numbers along the way.

However, when you move in the opposite direction (start from $0$ on the number line and move to the left), the numbers get smaller as you move along.

These exact rules apply to the negative side of the number line.

The numbers get larger as you move to the right and get smaller as you move to the left.

For example, since $-3$ is on the left side of $-2$, it is actually smaller than $-2$. We can write this with an inequality: $-3 < -2$.

On the positive side of the number line, $3$ is more positive than $2$, so $3$ is larger.

However, on the negative side of the number line, $-3$ is more negative than $-2$, so $-3$ is smaller.

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Now, try an example problem.

We know that the numbers get larger as you move to the right and get smaller as you move to the left. Let’s draw a number line and place these numbers on the number line.

Since $-1$ is the rightmost on the number line, it is the largest number.

It's that time again in Pittsburgh. The leaves have all fallen, the snow is starting to fall, and the temperatures are dropping—fast. One day it gets past freezing, $32^{\circ}$, then it drops towards the truly cold. First $20^{\circ}$, then $10^{\circ}$, then $5^{\circ}$.

But where do we go when it gets colder than even $0^{\circ}$?

Some types of film are developed by taking the opposite of every color on the actual photograph. By taking the opposite of the photograph, we can know exactly what the original looked like by reversing the colors again. But what do we call the opposites?

The solution to both of these, of course, is "negatives". Negative numbers are all the numbers that are less than $0$. This might seem weird, but we can think about it in a couple of different ways.

When you borrow more than you can pay

Say you had $\$5$, and you borrow $\$10$ from your friend. You then spend it all on a very delicious pizza (worth every penny). How much money do you have now? You don't have any cash on you, but you still owe your friend $\$10$. So we can only say that you have $-\$10$.

The "opposite" of a positive

A positive number and it's corresponding negative (the same number with a negative symbol out in the front) always combine to make $0$. Understanding that a negative number represents the opposite of its corresponding positive can allow you to grasp how to work with them.

This might be the number line you're used to seeing:

There's nothing incorrect about this number line. It's just incomplete. A more complete line would look like this:

Negatives on the Number Line

A negative number is any number less than $0$.

Negative integers are simply numbers below, or to the left of $0$ on the number line.

On a number line, negative numbers (on the left side of the number line) are simply a mirrored image of positive numbers (on the right side of the number line).

$0$ is the number that separates the positive and negative numbers.

The numbers get smaller as you move to the left of the number line, and get larger as you move to the right of the number line.

Let’s start with identifying negatives on the number line. Take a look at this example.

Starting at $-5$, we can count up by $1$ until we reach the marked number (the dot).

The marked number is $-3$.

We can also start from $0$ and count down by $1$ until we reach the marked number (the dot).

The marked number is $-3$.

Let’s try an example that compares negative numbers.

Let’s draw a number line and label $-5$ and $-7$.

The larger number is on the rightmost on the number line. Between $-5$ and $-7$, $-5$ is the rightmost number. Therefore $-5$ is larger.

We are now going to take a look at some of the types of problems you might encounter about negatives on the number line.

Since the increment on the number line is $2$ (each tick is a jump of $2$), we can count down from $-4$ by $2$ until we reach the marked number (the dot).

We know that the numbers get larger as you move to the right and get smaller as you move to the left of the number line. Let’s draw a number line and place these numbers on the number line.

Since $-6$ is the rightmost on the number line, it is the largest number.