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.

Main content

### Course: 6th grade>Unit 5

Lesson 1: Intro to negative numbers

# Introduction to negative numbers

Negative numbers are essential in math, representing values below zero. On a number line, they appear to the left of zero, opposite positive numbers. They're commonly used in real-world situations like measuring temperatures below freezing. Understanding negative numbers helps us grasp a broader range of mathematical concepts. Created by Sal Khan.

## Want to join the conversation?

• Why is your voice so cool Mr khan?
(67 votes)
• he is cool
(26 votes)
• How do you subtract positive and negative numbers ?
(17 votes)
• subtracting a positive is just counting sown from it but subtracting a negative is like the number is getting bigger just dont forget the (-) sign
(8 votes)
• Why are there negative numbers
(7 votes)
• Good question! Negative numbers allow us to subtract a larger number from a smaller number and get a meaningful answer. For example, without negative numbers, we can’t do 3 - 8. With negative numbers, we can do 3 - 8 to get the meaningful answer of -5.

In real life, negative numbers can represent debts (amounts of money owed), withdrawals from a bank account, losses, backwards offensive plays on a football field (for example the quarterback is sacked), temperatures below 0, and heights below sea level.

In chess, a number is often used to evaluate a position. A positive number represents an advantage for white, while a negative number represents an advantage for black.

If you ever study Vedic math, which is an Indian system of arithmetic and algebra tricks, you will sometimes encounter negative digits (symbolized with bars above the digits instead of negative signs in front of the digits).
(18 votes)
• Would negative numbers be the same as decimals…like -1 is equal to 1 ?
(6 votes)
• Negative numbers and decimals are not necessarily the same thing. For example, 0.8 is a decimal that is positive, and -5 is negative but has no decimal part.

Have a blessed, wonderful day!
(10 votes)
• why do we even need math in life is our life a math problem?
(11 votes)
• Hello Victoria!

In everyday life, we use mathematics for things such as incomes, and expenses, or home-task things. We also can use mathematics for science, and we are able to get great jobs with prior mathematic experience. Mathematics also appears all around us. There are much more things that we can use with mathematics, but I suggest for you to go read a article about it if interested.

Hope this helps!
(3 votes)
• If we use math for negative numbers... Can we use it for Negative degrees?
(7 votes)
• For Fahrenheit or Celsius temperatures, it is possible to have negative degree measurements for extreme cold.

For angles, usually only positive degree measurements are seen in geometry. However, sometimes negative degree measurements are seen in trigonometry. Clockwise represents the negative direction for angles in trigonometry.

Have a blessed, wonderful day!
(4 votes)
• Mom help the math man is rotting my brain!
(5 votes)
• You are wrong! Sal makes math fun. This man is a genius! Thanks Sal.
(7 votes)
• if the sky is orange on a Saturday and the wind is blowing diagonally how many lifeguards does it take to eat my fishes uncles hand collection?
(6 votes)
• penguin chair
(3 votes)
• homeschooled ;-;
(6 votes)
• idk how to do this
(6 votes)

## Video transcript

- [Instructor] In this video, we're gonna introduce ourself to the idea of negative numbers. Now you're already used to the idea of positive numbers. You just call them numbers, not positive (chuckles) numbers. And just to give you an example, I will draw a number line here. And this should all be review for you, so let me start at zero, and then this would be one. This would be two. This would be three. And you can think of these numbers, which you're used to, which we could call positive numbers, as how far we are above zero. One is one above zero. Two is two above zero. Now what do you think negative numbers are going to be? If positive numbers are how far we are above zero, then a negative number would be how far are we below zero. So for example, if I go one to the left on this number line, that would now get us to negative one. Positive one is one to the right. Negative one is one to the left. If I were to go another one to the left, I would get to negative two, and I could keep going. As many positive numbers there are, I can have the negative version of it. However far I am to the right, I could be that far to the left. Now some of you, especially if you live in very cold parts of the world, might have already experienced negative numbers in some way. For example, if you look at a thermometer, this has both a Celsius thermometer, right over here, and Fahrenheit. We know that you can get temperatures below zero degrees Celsius and temperatures below zero degrees Fahrenheit. On this thermometer, they just mark how far we are below zero with these red numbers, but really these are negative numbers. And we specify negative numbers by putting that negative sign right in front of it like that. So for example, 20 degrees Celsius is positive of 20 degrees Celsius is actually a pretty comfortable temperature, but negative 20 degrees Celsius, that is below, 20 degrees Celsius below the freezing point of water, that is a very, very, very, very cold temperature. One is 20 degrees above zero. One is 20 degrees below zero. So a big picture, for any given number, there's a negative version of it. For example, this right over here would be positive six, and then you could have negative six. But negative six is six below zero or six left of the zero on the number line, while positive six is, of course, six above zero. So I will leave you there. You might be thinking, "Oh wow, this looks a lot like a subtraction sign. Maybe it is related to subtraction somehow." Or "How can I do addition and subtraction, multiplication and division with negative numbers?" And for that we will go to future videos.