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# Absolute value word problems

Learn to solve word problems that ask us to apply our new absolute value knowledge. Created by Sal Khan.

Video transcript

The Statue of Liberty,
pictured above, is a gigantic sculpture
located on Liberty Island in New York, United States. The height of the
sculpture is 151 feet. So this distance right
over here is 151 feet. So it's like a 15 story
building or more, or about a 15 story building. The distance from the
ground to the torch is 305. So from here to
there is 305 feet. What is the absolute
value of the difference between 305 and 151? Well we just have to
subtract 151 from 305. And you might be able
to do that on your head. Let's see, if you add 150
to 151, you get to 301. So then you have to add
another 4, so it's 154. Or you could use a
calculator right over here. You could say 305 minus
151 is equal to 154, which is what we
did in our head. And the absolute
value of 154-- there's a couple of ways you
can think about it. You could learn to
just view it as, how far is that number from 0? And positive 154
is 154 away from 0. If this was negative
154 then that also would be 154 away from 0. The other way to
think about it is, whether it's
positive or negative, the absolute value,
you just take the positive version of it. So either way we say 154. Let's do a couple more of these. I like these pictures. The average weight of a
car in the United States is roughly 4,000 pounds. The dinosaur Ankylosaurus--
artist rendering above-- is thought to have weighed
up to 13,000 pounds. What is the absolute
value of the difference between these two weights? And you could calculate the
difference between these two weights. You could take the smaller
and subtract from the larger. So if you take
4,000 from 13,000, the difference would
be 9,000 pounds. The absolute value
of 9,000 is 9,000. You could have
gone the other way. You could've subtracted
13,000 from 4,000, and you would have
gotten negative 9,000. But the absolute value of
negative 9,000 is still 9,000. So we just want to think
about the absolute difference between these two. We don't want to
think about which one we're subtracting
from whichever one. Whatever we're subtracting
from the other one, we just find the
absolute difference. So whether the difference
was negative 9,000 or 9,000, depending on which one you
subtract from the other, the absolute value
of either of those is going to be 9,000 pounds. Let's do one more. No picture this time. I was getting used to that. The Panama Canal
is a canal cutting through the country of Panama
that conveniently connects the Atlantic and Pacific Oceans. What's nice about
these is we learn other things other
than mathematics here. France began constructing
the canal in the year 1881 and, after the French
abandoned construction, the United States finished
construction in 1914. What is the absolute value of
the difference between the year construction of the
Panama Canal started and the year that it ended? Well, there's a couple
ways you could do it. You could take the larger year
and subtract the smaller year from it. We have our calculator here. You could literally
say 1914 minus 1881, and you get 33 years. And the absolute value
of 33 is just 33. Or you could've done it
the other way around. Since we're taking
absolute value, it doesn't matter what we
subtract from the other ones. You could do on 1881
minus 1914, and you would've gotten negative 33. But the absolute value of
either of these numbers is, you're saying, how far
is 33 or negative 33 from 0? Well, they're both
33 away from zero. Or you could say, well, what's
the positive version of either of these? Well, it's 33. So the absolute value of
the difference in the years is 33 years. And we're done.