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# Ordering negative numbers

Sal puts -25, -30, -7, -10, and -40 in order from least to greatest. Created by Sal Khan.

Video transcript

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