If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Lesson 7: Comparing absolute values

# Negative numbers FAQ

## What are negative numbers?

Negative numbers are numbers that are less than zero. They have a negative sign ($-$) in front of them, like $-3$ or $-17$. Negative numbers can represent things that are opposite, missing, or below something else.
For example, if we own $5$ apples and we eat $2$ of them, we can say that we have $5-2=3$ apples left. But if we own $2$ apples and we eat $5$ apples, we can say that we have $2-5=-3$ apples left. That means we ate $3$ more apples than we had, or we owe $3$ apples to someone.
Negative numbers can also represent temperatures that are below freezing, heights that are below sea level, or debts that we owe.

## How do we compare negative numbers?

Comparing negative numbers means finding out which one is smaller or larger than another one. It works the same as comparing positive numbers. Numbers farther to the right (or farther up, on a vertical number line) are greater than numbers that are farther left (or down) on the same line.
To compare negative numbers, we need to remember that the farther left a number is relative to $0$ on the number line, the smaller it is. For example, $-3$ is smaller than $-$1, because $-3$ is farther left of $0$ than $-1$ is. We can write this as $-3<-1$ or as $-1>-3$.
We can also use the opposite numbers to compare two negative numbers. For example, the opposite of $-3$ is $3$, and the opposite of $-5$ is $5$. Since positive $5$ is farther right of $0$ than positive $3$ is, $5>3$. The negative numbers will have the opposite relationships, since they move left of $0$ instead. So $-5$ is less than $-3$, which we write as $-5<-3$.
A positive number is always greater than a negative number.

## What is absolute value?

Absolute value is the distance of a number from zero on the number line. It is always a positive number or zero. We write it with two vertical bars around the number. For example, the absolute value of $-3$ is $3$, and the absolute value of $3$ is also $3$. We can write this as $|-3|=3$ and $|3|=3$. The absolute value of $0$ is $0$, since there is no distance between $0$ and itself.
The absolute value of a rational number is the same as the value of the number without the sign. For example, the absolute value of $-1.25$ is $1.25$, and the absolute value of $0.75$ is $0.75$. We can write this as $|-1.25|=1.25$ and $|0.75|=0.75$.

## Where do we use negative numbers in the real world?

Negative numbers and absolute value can help us describe and measure many things that we encounter every day. Here are some examples of where we use negative numbers and absolute value in the real world:
• We use negative numbers to show temperatures that are below freezing, like $-10\mathrm{°}$ Celsius or $-15\mathrm{°}$ Fahrenheit. We can also use negative numbers to show how much colder or warmer a place is than another place, like $-5$ degrees difference or $-10$ degrees difference.
• We use negative numbers to show heights that are below sea level, like $-100$ meters or $-300$ feet. We can also use negative numbers to show how much deeper or higher a place is than another place, like $-50$ meters difference or $-150$ feet difference.
• We use negative numbers to show debts that we owe, like $-\mathrm{}500$ or $-\mathrm{}1000$.
• We use negative and positive numbers to show movement in specific directions, like saying that we moved $-10$ seconds in a video to mean that we went $10$ seconds backwards in the video. If moved $10$ seconds forward in the video, we could use positive $10$.
The absolute value tells us the amount of the change in each case, but removes the information about the direction of the change. For example, the absolute value of a height could tell us its distance from sea level, but would not tell us whether the object was above or below sea level.

## Want to join the conversation?

• I wonder why they didn't put practice questions?
• It is an FAQ not a review.
• who invented negative numbers? are those the only times we use them?
• *In the seventh century, an Indian mathematician named Brahmagupta is said to be the first to write rules for negative numbers. He wrote about negative numbers in addition, subtraction, multiplication, and division!*
• so you are saying that i can use it in the real world
• Yes, Negative numbers and absolute value can help us describe and measure many things that we encounter every day. Here are some examples of where we use negative numbers and absolute value in the real world:
We use negative numbers to show temperatures that are below freezing, like

Celsius or

Fahrenheit. We can also use negative numbers to show how much colder or warmer a place is than another place, like

degrees difference or

degrees difference.
We use negative numbers to show heights that are below sea level, like

meters or

feet. We can also use negative numbers to show how much deeper or higher a place is than another place, like

meters difference or

feet difference.
We use negative numbers to show debts that we owe, like

or

.
We use negative and positive numbers to show movement in specific directions, like saying that we moved

seconds in a video to mean that we went

seconds backwards in the video. If moved

seconds forward in the video, we could use positive

.
The absolute value tells us the amount of the change in each case, but removes the information about the direction of the change. For example, the absolute value of a height could tell us its distance from sea level, but would not tell us whether the object was above or below sea level.
(1 vote)
• how do you eat 5 apples but only have 2 apples instantly
• can you stop hurting my brain pls?
• are we going to actually need this in any other job than a bank
• yes because you proble wnat to keep track of you money and other stuff like legos so you don't have 900000 candy bars in loan from your little brother.
• I owe someone 3 apples :(
but I dont have any apples! :'(