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:
"Ah well, you know - 40 - 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 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 owed the bank only $7,
so it's actually the case that -40 is less than -7, and
out of all of these numbers, it is the least of all of them.
So -40 is the very least,
and you can view that as 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 -30,
and then the next smallest after that would be -25,
and then the next smallest after that would be -10,
and then finally the greatest of all of these numbers
(--the greatest, and I will do it in pink--)
...the greatest of all of these numbers is -7.
And if it's still not obvious to you,
you could also think of them in temperature,
in temperature terms.
Which of these is the coldest temperature?
(whether you're talking about Celsius or Fahrenheit)
-40 would be the coldest temperature,
and -7 would be the warmest temperature.
There would be the most heat in the air at -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 you know, we could put maybe +7 up here,
+7 isn't one of these numbers,
but we can plot all the other numbers.
So this right here might be -7.
If that's -7 then maybe this right over here would be -10.
Notice we go further and further to the left of the zero,
and then we go a little bit further to the left we get -25...
A little bit further to the left than that is -30.
Then you go even further to the left and you get to -40.
If you think about 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 furthest to the right.