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Introduction to negative numbers

Sal introduces the concept of negative numbers using number lines and real-world situations. Created by Sal Khan.

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  • male robot donald style avatar for user shaardul basnet
    Why is your voice so cool Mr khan?
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  • aqualine ultimate style avatar for user Banana Allyson
    How do you subtract positive and negative numbers ?
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    fortnight battle pass
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    Down in ohio
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    Why are there negative numbers
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    • primosaur seed style avatar for user Ian Pulizzotto
      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).
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  • old spice man blue style avatar for user VictoriaS
    why do we even need math in life is our life a math problem?
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    Thank you for making me suffer
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  • starky sapling style avatar for user Ellie WingsOfFire Nerd
    I do not get it.... Do we just count back 0 like 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10?
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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.