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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 <i>owe</i> 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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<i>-40</i> 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.