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Subtracting by adding on

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okay boys and girls let's practice subtracting by adding on now first of all let's talk about why this strategy works  what's look an example of a subtraction problem 10 - 3  now when were solving 10-3 there's two ways to think about that we can think of it as starting with 10 and taking away three we could also think of it as finding the distance between 10 and 3 that distance is also called the difference the same label that we gave to the answer to a subtraction problem so if I think about this is 10 - 3 I end up with 7:10 987 Camelback  or if I were to think about this is finding the difference between 10 and 3 I could count backwards from 10 back to 387-6543 and we would have counted seven number so either way or difference is 7 so let's take a look at using the same numbers but in an addition equation if I were to example begin with three and count on up to 10 I would end up counting that same difference of 7 so what that shows us is that whether we're starting higher number in counting backwards or starting with the lower number and adding up the difference or the distance between two numbers is always the same since it's going to be the same going either down or up that means that we can actually add to subtract because no matter what we're going to be play the difference between the beginning number and the ending number the same thing that we do when we subtract so this strategy says that fact to turn a subtraction problem around into an addition equation this strategy is great for people who prefer to you addition instead of subtraction you can actually use addition for subtraction here we see an example already -3 would be the same as 3 plus something equals 10 in either case we get the same answer and it shows of how to turn a subtraction equation into an adding an equation the larger number that we end wit or begin with Excuse me become number that we end with the number we are subtracting becomes the number that we start with and then we add on from that smaller number up to the number now we do have some strategies for where and how we want to do that let's look at a larger problem that's going to serve as a better example Morris let's write a problem that similar to the types of subtraction problems we've been doing in class  5146 2378 Mustang our first step with this strategy is to take or subtraction equation and turned into an adding on equation so member we're going to start with the smaller number  see how much we have to add on to get all the way to the larger number  so here's my adding on equation that is exactly the same as our subtract equation okay so we're going to begin with that smaller number and we're going to stop in certain places since hundreds and thousands are easier to work with we're going to stop first at the next 10 going up now when I look at the number that we're starting with two 378 I want to focus in on the tens place to think about what the next ten would be since right now we have seven tens 70 that mean the next 10 going up is 80 but of course it's not just 80 it's 2380 so we ran our 2000 and then now we think okay how much do I have to count on from 2378 to get to 2380 I'll give you shortcut just count from 78 up to 80 when we do that we'll see that it takes to one's so so far we know one part of our difference we know that the difference is two ones and we've gotten to 2380 so now that becomes are starting number for our next problem stop there and now we're going to continue to another number now we're going to go on to the next hundred just like we looked at the tens digit to figure out the next 10 going up my beat now we can look at the hundreds digit to figure out what the next 100 going up might be right now we have 2380 if we think about adding one to the hundreds place that would make 400 but of course we would not still have the 80 because hundreds only have thousand hundreds tens and ones  so we end up over here with 2400 then we think okay if I have 80 I'm going to be adding up enough to make another hundred how much do I have to add well at is eight tens another hundred would be ten tens so we need two more times  20 all right now we have two parts of our difference and we've landed at mm 400 so that becomes the starting number for our next step now we're going to add from there on to the next thousand we can look at our thousands digit for that this work we have 2,000 right now the next thousand going up would be exactly 3000  once again we can use the fact that our number system is this tends to think about how many more hundreds we need to make this extra thousand a thousand is made of ten tens or skews me a thousand is made 10 hundredths Arden B boys and girls we already have 4 of those hundreds so if we were to count on to a thousand we would count 500 600 700 800 900 1000 who would have counted on 600 or 600 on there known our final step we can go from that thousand up to the higher number that was in our problem in this problem that I have to 146 so that becomes the number we add up to in the final step  this step even though I might look is actually the easiest I start with 0 ones I end up with 6 so I must have had at 6 I started with zero tens ended up with 4 so I'm added tens I started with 0 hundreds and it up with one so I must have added 100 I started with three thousands what the five top means that I added 2000s  so now I have all the pieces of my difference and look at that if I was careful enough my digit should all be lined up in a way where I can now add the ones tens and hundreds together without having to rewrite these numbers so let's do that in the place I have 20016 adding 2 + 6 which makes eight ones  in the tenths place I'm adding to zero or which really means I'm just adding to in for which makes 6 tenths in the hundreds place we have six and one which makes 7 in we only have those two thousands so there we have used the pieces of the difference that we found by adding on to find the total difference 2007 endured 68 so I would be sure to write that up here  chicken plate my equation  alright boys turn off I hope that video helps you with the subtracting by adding on strategy

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