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# Solving 3-digit addition in your head

## Video transcript

what I want to do in this video is go over some techniques for doing mental addition now if I saw something like 355 plus 480 if you have some paper around you could write write these numbers down and do your traditional addition but you might want to be able to do these in your head so how do you do it well the way to think about it is can we can we add or subtract from these numbers so that one of these numbers might become a little bit a little bit simpler so for example I have 480 here what would I have to do to 482 say get it to 500 it's almost 500 well I could add 20 to 480 but I can't just add 20 I would have to also take away 20 so what happens if i take away 20 from from 355 and add it to 480 so what am I talking about so this is going to be the same thing as so let me take away 20 from this so that's going to be 3 35 3 35 and let me add 20 to this so 480 plus 20 is 500 and the whole reason why I took away 20 and I added 20 as I said well what do I have to add to 480 to get to 500 and I could have done that in my head okay I need to add 23 55 minus 20 is 335 but now this problem is much much simpler to compute 335 plus 500 well it's going to be 300 plus 500 it's going to be equal to its going to be equal to 800 and then we have 35 835 now to make it a little bit clearer what we did remember we wanted to take 20 from here and put it over here so we could break up 355 we could say that it's going to be equal to it's going to be equal to let's break it up into 335 and 20 and remember the whole reason why I pick 20 is because I'm going to want to add that to 480 but I'm just doing it step by step here so plus 480 and now I can just change the order with which I add so I could say this is going to be equal to 300 35 plus 20 plus 480 plus or 80 instead of adding the 335 and 21st I could have the 20 and 480 first so I could add I could add these two characters first and so then I'm going to be left with this is going to be equal to three hundred thirty-five plus what's twenty plus four eighty well that was the whole point I picked twenty so that I can get to five hundred twenty plus four or eighty is going to be five hundred and then now you can add them this is going to be eight hundred and thirty-five so this is just a longer way of saying what I did here I took 20 from 355 so I can make the 480 into a 500 let's do a couple more examples of this and remember the key is just thinking about how could I add or take away from one of the numbers to make them simpler so over here I have 18 plus 704 so there's a couple of ways we could tackle this one way we could try to get the 704 to be equal to 700 so we could say we could say that this is the same thing as 18 plus 18 plus I could write 700 plus 4 or I could write it as 4 plus 700 like that and then I could and I could put the parentheses around this first and then I could just switch the order in which I add so this is the same thing as 18 plus 4 plus 700 and now I could do I could add the 18 and the 4 first now what's 18 plus 4 it's 22 and then I have plus 700 plus 700 and now this is pretty easy to compute and all of these are going to be equal to each other so let me just write it like that 22 plus 700 I can do that in my head that's going to be 722 now I know what you're thinking eh this is supposed to be a technique for doing something in my head I don't have I can't write all this stuff down in my head the reason why I'm writing this down this way is that you see what's really going on but you could do it a lot quicker you could just say hey let me take 4 from the 7 just I'm closing my eyes right now as I'm talking just so I can pretend like I'm doing it in my head ok let me add 4 to 18 and take away 4 from 700 well that's going to be this if I add 4 to 18 this is going to be 22 and if I take away for from 704 that's going to be plus 722 plus 700 is 722 now there's another way that you could tackle it you could say well let me actually instead of taking away 4 let me add some number some value here so I get to I don't know say 710 that seems a little less ideal for me but you could do it well let's see if I added six to 704 I'll get to 710 so how about I break off 6 from the 18 and add it to the 704 so I could write it like this I could say 18 is the same thing as 12 plus 6 and then plus seven oh four plus seven oh four which is the same thing as 12 plus 6 plus plus 704 and then I could add these first and I could have 12 plus 710 710 and I might be able to say okay that's going to be 722 but this method right over here doesn't seem anywhere near as intuitive as doing this is trying to get the hundred trying to get the 704 to 700 by taking 4 from here and adding it and adding it over here let's do let's do one more example of this so 275 plus 595 well my gut reaction is can we get this 595 to be equal to 600 so this is going to be equal to so if I add 5 to 595 I get 600 let me do it in that same color so I'm going to add 5 to it to get 600 I have trouble switching colors so 600 but I can't just add 5 here I'd also have to take 5 away from here so taking 5 from there that would be 270 so this becomes 270 plus 600 and this is easier for me to compute in my head this would be 200s plus 600 is equal to 800 I have 7 tens plus 0 tens so 800 and then have no ones 870 now another way that you could have tried to tackle it is like let's try to get this 275 to let's try to get it to 300 so we could say this is the same thing as 300 we could say this is the same thing as 300 and to get there I just added 25 but if I add 25 from this number I don't have to take 25 away from this number so I could subtract 25 from here and then I would get 300 plus 95 minus 25 is going to be 70 so it's going to be five hundred and seventy five hundred and seventy and this is also easy to compute three hundred plus five seventy is eight seventy and there's other ways that you can tackle this including the traditional way of writing it down on paper and whatnot but hopefully this gives you a little bit of a toolkit for being able to solve these things maybe in your head