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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.