ShmoopTube

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Ever felt like a zero?

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Yeah. Not fun. [Man on a bench with his head in his hand]

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Now can you imagine feeling like LESS than a zero?

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Seems impossible, doesn’t it? Well, thanks to the number line, nothing is impossible. [Number line waving]

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You see that? number line just totally made the statue of liberty disappear.. Incredible!

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When it comes to numbers, they don’t just represent stuff you can see, or hold in your

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hands.

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“One” is easy to wrap our heads around, because we can see one of something. [Man wraps number 1 around his forehead]

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But…negative 1? What in the world is that?

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Negatives are actually used to help us understand some pretty complex ideas by allowing us to

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assume that every positive number has a partner on the opposite side of zero on the number line. [positive and negative numbers on a number line]

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But for now…don’t worry about those complex ideas.

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The important thing is to understand the basics of how negative numbers work.

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You know you’re looking at a negative when you see a number preceded by a negative sign…

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one of these little dashy things. [negative symbol circled]

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If we see negative 3, for example, that symbol is telling us that this number exists three

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units to the left of zero on the number line.

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If we see negative 455, well…we’re going to need a bigger monitor. [dog walking on a beach]

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What happens when you add one negative number to another?

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By adding two negatives, we’re basically saying, “Hey…if we start this many units

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left of zero…and then we go x number of units further away from zero…where will

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we end up?”

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The answer? Pretty darn far away from zero.

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Like… negative 5 plus negative 6 is negative 11. [-5 + -6 calculation above a number line]

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Just as, on the other end of the number line, 5 plus 6 is positive 11.

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When we subtract one negative from another, on the other hand, the signs cancel…

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…and the result is that we’re actually moving in the direction of zero.

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Negative 8 minus negative 3 is the same as negative 8 plus positive 3…

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…or negative 5.

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If we start with negative 1 and subtract negative 7, we’ll cross over zero completely and [negative 1 circled on a number line]

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wind up at positive 6.

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Don’t forget to stop and say hi to zero on the way. It gets awfully cranky when it [man with number zero for a face looking cranky]

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feels ignored. Okay, now what about when we add one positive

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and one negative?

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“Adding a negative” is really the same as subtracting…

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…so 9 plus negative 4 is another way of saying 9 minus 4…which is 5.

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Ine-nay inus-may orr-fay is yet another way of saying 9 minus 4, but… it won’t help [pig talking]

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us here, so let’s move on. If you ever add a negative number to its corresponding

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positive number, you’ll get zero. Every. Time.

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Go ahead. Try a few hundred of ‘em. You’ll see. [young child sleeping]

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Finally, you can multiply or divide negatives.

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Whenever you multiply or divide one negative by another negative, the signs will cancel out

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and you’ll come up with a positive result.

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One positive and one negative…and the result will be negative.

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Commit these rules to memory, and you’ll be well ahead of the curve.

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Well, ahead of the line anyway. [Number line takes off top hat and is squashed by statue of liberty]

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Isn’t he marvelous?

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