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# Subtracting different ways

## Video transcript

let's review a little bit about what we know so far about subtraction so if I say five minus three what does that mean well there's a couple of ways to think about it I could have five let's say I had five five berries so one two three four five so I could have five berries and when I say minus three or subtracting three from it I can view that as saying I'm going to take away three of these berries so if I take away that berry that berry in that berry so I've took away one two three berries how many berries do I have left well the only berries I have left or right here one two so I have two berries left just like that now the other way the other way that I could visualize or think about five minus three I'll do it over here five minus three it's just think about what the difference between five and three is so let me do this so let's say I have five berries one two three four five and let's say that you have three berries here's a slightly different color you have three berries so another way to think about five minus three is how many more berries do I have then you have and if you look right here well you see this berry is another you have also one berry there we both have one berry there we both have one berry there but I've got one two berries that you don't have so once again I have two more berries than you have now we can also think of this in from the number line point of view the number line point of view so let me draw a number line just like that it's my number line we've learned on the Edition videos we can keep going off forever and actually we can even go to the left of zero and go into negative numbers which we'll see in future videos but I'll start at zero zero one two three four five I'll just go I'll go up to seven so if we do five minus three if we view three is being taken away from five five minus three means start at five if I did five plus three I would go I would jump three spots to the right because that's increasing the number of things I have but if since I'm subtracting three I want to decrease by three so I decrease by one two three and I get to I get to two just like that now if we visualize it from this point of view let me draw another line number line I wanted to show you I mean this is I'm taking away 3 and here I'm saying how many more is 5 then 3 even though that they are the exact same answer but there are two different ways to think about it let me draw a number line here again we draw the same number line I'll draw the same number line I have 0 1 2 3 4 5 6 7 so if I were to plot where 5 is on this number line so this is the 5 right there little pink square around it 5 is right there now 3 let me do 3 in this yellow color 3 is right here on the number line so in this this way of thinking about 5 minus 3 you're saying how far what is the difference let me write that down here we're saying what is the difference the difference between 5 & 3 between 5 & 3 & to figure out the difference you actually have to say how much do you have to add to 3 to get to 5 so the difference here how different is 5 then 3 well you have to go up 1 and then up 2 to get to 5 so the difference between 5 which is all the way over here and 3 which is just that far is the difference between 5 & 3 is 2 just like that that right there is to let me draw that in another box so that's 2 right here and I want to make these these this difference between subtraction and difference I wanna make it at least reasonably clear to you because this is this these are two different ways of viewing subtraction but it ends up being the exact same operation you're gonna get the same answer regardless of which way you think about it now I could view let me do different numbers now we do seven minus four so I could view this as maybe I have a seven foot long piece of wood maybe I have a seven foot long piece of wood it's seven feet long let me know if I put a ruler up against it I would have that's zero one two three four five six seven so I have a seven foot long piece of wood and then I could saw off four of those feet so if I were to saw four of these feet so I sawed off one two three four how much wood do I have left so all of this stuff right here I'm eliminating I'm sawing it off I'm sawing it off of the wood maybe I should do that in a darker color to show that I'm that to show that I'm sawing it off so all of this stuff is going to disappear I'm grinding it away I'm sawing that off so I'm just left with after I soft the four inches or feed or whatever of the wood I'm left with one one to three inches of wood so this is three so seven minus four is equal to is equal to 3 this is viewing subtraction is literally taking away I saw it off the wood so I took away wood now I could think of it in a slightly different but a slightly different way of thinking about it but give you the exact same answer we could say seven minus four so once again I could have the seven inch long piece of wood right like that so if I put a ruler here that's one one two three four five six seven so once again a seven inch long piece of wood and now instead of taking four away of it I'm comparing it so this des to seven I'm comparing it to a four inch long piece of wood so I have another four inch long piece of wood right there that's my four inch long piece of wood that's seven this is four you could view seven minus four is taking four inches away from the long piece of wood or you could view seven minus four is the difference between the four inch piece of wood and the seven inch piece of wood so in this case what's the difference to go from the four inch piece of wood to the seven inch piece of wood I would have to grow by three or I would have to add or I would have to add a three-inch piece of wood somehow for the wood would somehow have to grow by three inches in order to become seven inches so these are two completely equivalent ways to view subtraction that's all a little bit of review from the last video now what I also want to do in this video is start tackling slightly larger problems but you'll see that it really the number line applies just equally as well as to kind of the simpler problems that we've done before so let's do let's do 17 minus 9 so just like everything else there's two ways we could have done it you know the more slow way is you could draw 17 objects let's say I have 17 chips 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 and then I'm going to take away 9 of them so I'm going to take away 1 2 3 4 5 6 7 8 9 how many am I left with I'm left with 1 2 3 4 5 6 7 8 so 17 minus 9 is equal to 8 but that took a long time and you could imagine if this number was a lot bigger would have taken me forever to draw all of these circles and then scratch out things and it would've wasted paper and in time and well we have other things to do so another way you could do it and maybe this would be easier for you to visualize is to draw the number line you always don't have to start at 0 so if we draw the number line if we say let's say this 18 17 16 15 14 13 12 11 10 9 8 7 you could have met I could keep going to the left all the way to 0 but I start at 17 I could start at 17 and take away 9 from it so I go 1 2 3 4 5 6 7 8 9 and once again we are left at 8 now this was at least in my head a little bit cleaner and faster than this one but in either case you don't want to do this every time you have to subtract 9 from 17 or want to find the difference between 17 and 9 and then to realize that's 8 so this is something that eventually you'll want to internalize you what you'll want to know by heart that oh 17 minus 9 I know that is 8 and by the way 17 minus 8 what's 17 minus 8 well that is 9 and now why does all of this make sense because 8 8 plus 9 is equal to 17 so 17 minus 9 is 8 17 minus 9 is 8 or 17 minus 8 is 9 when I say 17 minus 8 I'm essentially saying that is equal to some number that if I were to add to 8 will equal 17 well that's 9 when I say 17 minus 9 that's saying there's some number that if I were to add it to 9 I'll get 17 well that's 8 so all of these all of these statements are kind of saying the same thing that 8 plus 9 or 17 or the difference between 17 and 9 is 8 or the difference between 17 and 8 is 9 hopefully hopefully I'm not confusing so for most of these for most of these subtraction problems where the answer is a one digit answer you you should you should eventually have the memorize but in your head it's good to be magining this number line let's do a couple more of these and then once we get once we have these memorized or at least be able to do a number line if we don't if we forget I'll show you how to do any subtraction problem for arbitrarily for super large numbers so let's say that let's say we're going to do 13 minus 5 so once again I'm not going to do the whole circles or the berries this time I'm just going to draw the number line just draw the number line like that and let's start it know this is 14 13 12 11 10 nine eight seven six five and you just keep going lower and lower you can go to zero or you could even go past as you or we'll talk about that in the future but we start at 13 we're starting at 13 13 and we're going to take five away from it so this is the subtraction view of subtraction we're taking away one two three four five and we land at eight so 13 minus five we do this in a new color 13 minus 5 is equal to 8 now another way we could have thought about that I plotted where 13 is I can plot where 5 is I could say look this is 5 5 is right here on my number line what do I have to add to 5 to get to 13 so let's see I have to go 1 2 3 4 5 6 7 8 I have to add 8 to 5 to get to 13 5 plus 8 is equal to 13 so that tells me that 13 minus 5 is equal to 8 this also tells me that 13 minus 8 is equal to 5 these are all all of these are on some level telling me the exact same thing but the difference between 13 and 5 is 8 the difference between 13 and 8 is 5 5 plus 8 is 13 so hopefully have the hang of that if you haven't done so already it'll be good to practice all of these you know take taking a teen number and then subtracting of any of the one digit number from those teen numbers that's in general very very good practice for you