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I've got five numbers here
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and the goal is to order them from least to greatest.
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And it might be obvious to you
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that all five of these numbers are negative numbers.
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So let's just think about which of these is the greatest number.
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And you might be tempted to say:
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"Ah well, you know - 40 - if these were all positive:
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40 would be the greatest."
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So you might be tempted to say "negative 40 is the greatest."
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But you have to realize what the negative is telling you.
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And think about that, think about...
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if these were your dollar amounts in your bank account...
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...would you rather have negative $40 in your bank account
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or negative $7 in your bank account?
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Negative 40 means that you owe the bank $40,
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so it's $40 less than having nothing.
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Negative 7 would mean that you owed the bank only $7,
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so it's actually the case that -40 is less than -7, and
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out of all of these numbers, it is the least of all of them.
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So -40 is the very least,
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and you can view that as the least amount of money
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that you would want, out of these comparisons,
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in your bank account, or the smallest amount of money.
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You owe the bank $40.
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Not only do you have nothing, you owe the bank $40.
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Then the next smallest number would be -30,
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and then the next smallest after that would be -25,
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and then the next smallest after that would be -10,
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and then finally the greatest of all of these numbers
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(--the greatest, and I will do it in pink--)
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...the greatest of all of these numbers is -7.
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And if it's still not obvious to you,
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you could also think of them in temperature,
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in temperature terms.
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Which of these is the coldest temperature?
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(whether you're talking about Celsius or Fahrenheit)
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-40 would be the coldest temperature,
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and -7 would be the warmest temperature.
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There would be the most heat in the air at -7.
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Another way to think about it is we could draw a number-line.
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--So let's draw a number line right over here--
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If this is a zero, and you know, we could put maybe +7 up here,
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+7 isn't one of these numbers,
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but we can plot all the other numbers.
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So this right here might be -7.
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If that's -7 then maybe this right over here would be -10.
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Notice we go further and further to the left of the zero,
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and then we go a little bit further to the left we get -25...
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A little bit further to the left than that is -30.
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Then you go even further to the left and you get to -40.
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If you think about it this way,
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the least of these numbers is the one that's furthest to the left
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on the number line,
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and the greatest is the one furthest to the right.