Absolute value word problems

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 if you add 150 151 you get to 301 so then you have to add another four so it's 154 or you could use a calculator right over here you could say 305 minus 151 is equal to is equal to 154 which is what we did in our head and the absolute value of 154 the absolute value there's a couple of ways you can think about it you can literally just view it as how far is that number from 0 and 154 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 154 154 let's do a couple more of these I like these pictures the average weight of the car of a car in United States is roughly 4000 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 larger 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 have subtracted 13,000 from 4,000 and you would have got 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 it's whether the difference was negative nine thousand or nine thousand depending on which one you subtract from the other the absolute value of either of those is going to be nine thousand 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 as 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 you might want to just you know if we just did the way that they well there's a couple of 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 that's a the absolute value of 33 it's just 33 or you could have done it the other way around since we're taking absolute value it doesn't matter what we subtract from what up from the other ones you could do on 1881 minus 1914 and you would have gotten negative you've got negative 33 but the absolute value of either of these numbers is you're saying how far is 33 or negative 33 from zero 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 33 years and we're done