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### Course: 7th grade > Unit 4

Lesson 4: Addition & subtraction word problems with negatives# Negative number word problem: temperatures

Use a number line to solve a word problem that includes a negative number. Created by Sal Khan.

## Want to join the conversation?

- At2:38Sal mentioned the absolute value. What is the absolute value?(16 votes)
- The absolute value is the distance a certain number is from 0. For example, the absolute value of 5 is 5, because it is 5 units away from zero. The | | symbols represent absolute value, so if you have something like |-9|, you find the absolute value of -9, which is nine.(31 votes)

- math is.... interesting..(14 votes)
- NutterButter(6 votes)
- It's been a long time since anyone has asked a question(5 votes)
- why do we need the vertical number line thought?(4 votes)
- This is because this problem is about temperature. Sal made the number line to resemble a thermometer.(3 votes)

- Quick question, Arn't number lines supposed to be horizontal?(1 vote)
- A number line is usually thought of as horizontal, but could be vertical. Note, for example, that the standard two-dimensional coordinate system is generated by the x-axis (a horizontal number line) and the y-axis (a vertical number line).(6 votes)

- this is a pain even more of a pain as taxes im gonna hav to do(4 votes)
- math makes me want to cry(4 votes)
- At2:38Sal mentioned the absolute value. What is the absolute value?(2 votes)
- The absolute value of a number, denoted by a pair of vertical bars, is its non-negative distance from 0 on the number line. This means we leave the number as is if the number is non-negative, but we remove the negative sign if the number is negative. For example:

|0| = absolute value of 0 = 0.

|5| = absolute value of 5 = 5.

|3.2| = absolute value of 3.2 = 3.2.

|2/3| = absolute value of 2/3 = 2/3.

|-5| = absolute value of -5 = 5.

|-3.2| = absolute value of -3.2 = 3.2.

|-2/3| = absolute value of -2/3 = 2/3.

Have a blessed, wonderful day!(4 votes)

## Video transcript

One of the coldest temperatures
ever recorded outside was negative 128 degrees
Fahrenheit in Antarctica. One of the warmest
temperatures ever recorded outside was
134 degrees Fahrenheit in Death Valley, California. How many degrees
difference are there between the coldest and warmest
recorded outside temperatures? So let's think about
this a little bit. Now, what I'll do is I'll
plot them on a number line. But I'm going to plot it on
a vertical number line that has a resemblance
to a thermometer, since we're talking
about temperature. So I'm going to make my number
line vertical right over here. So there's my little
vertical number line. And this right over here
is 0 degrees Fahrenheit, which really is of
no significance. If it was Celsius,
we'd be talking about the freezing point. But for Fahrenheit, that
happens at 32 degrees. But let's say this is
0 degrees Fahrenheit. And let's plot these two points. So one of the
coldest ever recorded temperatures was negative
128 degrees Fahrenheit. So let's say that's
right over here. This is negative 128
degrees Fahrenheit. And one of the warmest
temperatures ever recorded was 134 degrees. This is a positive 134. So it's about that far
and a little bit further. So it's a positive 134
degrees Fahrenheit. So when they're asking us
how many degrees difference are there between the
coldest and the warmest, they're essentially
saying, well, what is this distance
between the coldest and the warmest right over here? What is this distance? And there's a couple of ways
you could think about it. You could say, hey, if I started
at the coldest temperature and I wanted to go all
the way up to the warmest, how much would I have to add? Or you could say, well,
what's the difference between the coldest
and the warmest? So you could take
the larger number. So it's, say, 134. And from that, you could
subtract the smaller number, which is negative 128. So this essentially
saying what's the difference between
these two numbers? It's going to be positive,
because we're subtracting the smaller one
from the larger one. This is going to give you
the exact same thing as this. Now, there's several
ways to think about it. One is we know that if you
subtract a negative number, that's the same thing as adding
the positive of that number, or adding the absolute value. So this is the same thing. This is going to be equal to
134 plus positive 128 degrees. And what's the
intuition behind that? Why does this happen? Well, look at this
right over here. We're trying to figure
out this distance. This distance is 134
minus negative 128. And if you look at
that, it's going to be the absolute value of 134. It's going to be this distance
right over here, which is just 134-- which is just
that right over there-- plus this distance
right over here. Now, what is this distance? Well, it's the absolute
value of negative 128. It's just 128. So it's going to be that
distance, 134, plus 128. And that's why it made sense. This way, you're
thinking of what's the difference between a larger
number and a smaller number. But since it's a smaller
number and you're subtracting a negative,
it's the same thing as adding a positive. And hopefully this gives you a
little bit of that intuition. But needless to say, we can now
figure out what's going to be. And this is going
to be equal to-- let me figure this out
separately over here. So if I were to add 134
plus 128, I get 4 plus 8 is 12, 1 plus 3 plus 2 is 6. It's 262. This right over here
is equal to 262. How many degrees
difference are there between the coldest and warmest
recorded outside temperature? 262 degrees
Fahrenheit difference.