Learn about Subtracting decimals

Khan Academy Presents: Subtracting decimal numbers

Welcome to the presentation on subtracting decimal numbers. Let’s get started with some problems. First problem I have here says 5.73–0821 equals who knows? So the first thing you always want to do with decimal like this and actually kind of inadvertently did this is it you want to line up the decimals. You actually want this decimal be right above this decimal and I almost did that one when I did it. It must have been my subconscious doing it but let me just do it a little bit neater. So it’s 5. 73 then I’ll put the decimal here, 0821. Some people say it always good to put zero in front of the decimal. My wife is a doctor and she says it’s critical otherwise you might give some of the wrong medicine. But anyway so we’ve lined up the decimals and now we’re ready to subtract. So one thing that you have to think about when you do decimal is we’re going to have to subtract this 21 ten thousands or this two and this one from something. We can’t just subtract it from this blank space. We have to add two zeroes here and as you know with the decimal when you add zeros to the end of it, it really doesn’t change the value of the decimal. So at this point we just viewed this like level for subtraction problem. So the first thing we do in any subtraction problems is see if any of the numbers on top are smaller than any of the numbers on the bottom. Well, in this case there are a lot of them. So zero is less than this one, this zero is less than this two, this three is less than this eight so we’re going to have to borrow and some people like to do their borrowing and subtracting they kind of alternate between the two. I like to do all my borrowing ahead of time. So what I do is I start on the top right and I say, “Okay, zero is less than one” so that zero becomes a ten but in order to become a ten I would have to borrow one from some place. I look to the left of that zero and say, “Well can I borrow the one from zero?” Well no, this is just the way I do it. There are other people who would actually let you borrow the one form zero but I say no. Instead of borrowing the one from the zero I borrow the one from this entire thirty. So this thirty, you see right there are three zeroes so I'm going to borrow one from it and it becomes twenty nine. We borrowed one from this thirty to get a ten here and now let’s check again to see if all our numbers on top are larger than all numbers on the bottom. Well ten is larger than one, nine is larger than two, two is not larger than eight so we’re going to borrow again so if we’re going to borrow two becomes a twelve and the seven we borrowed one from that becomes six. Let’s check again, ten is larger than one, nine is larger than two twelve is larger than eight, six is larger than zero and five is larger than zero. So now we’re done all our borrowing and we’re ready to do some subtraction and this is the easy part, ten minus one is nine, nine minus two is seven, twelve minus eight is four, six minus zero is six, and five minus zero is five. Now we just bring down the decimal point. There is our answer, 5.73–0.0821 = 5. 6479. There you go I probably confused you, so let’s do more problems. Here’s another one. Let me leave some space on top to the borrowing, 8.25–0.0105. So what was that first step that I always have to do? Right, to line up the decimal so let me do that. So it’s 8.25–0.0105. Now that’s lined up with this decimal right below this decimal. Now I add the zeroes just because this zero and this five needs to be subtracted from something and now let do my borrowing. Now once again all I do is check to see whether the top number is larger than the number below it. This is zero is smaller than five so I'm going to borrow. I can’t borrow from this zero so I have to borrow from this entire 50. So if I borrow one from 50, I get 49 and this zero will then become a ten right. I borrowed 1 from 50 to get a 10. Now am I done? Ten is larger than five, nine is larger than zero, four is larger than one, two is larger than zero and eight is larger than zero. So I think I'm ready to subtract, ten minus five is five, nine minus zero is nine, four minus one is three, two minus zero is two and eight minus zero is eight and I bring down the decimal point. If you mastered the level four subtractions the decimal problems really are just about lining up the decimal point adding the zeroes and just doing normal subtracting problem. In general, with subtraction I think most people have the most trouble with the borrowing. The way I do it I think is a little bit different than is taught from lot of schools. A lot of schools they’ll do the subtraction they borrow alternatively. But I found this easier when I just borrow ahead of time and I also like for example this problem when I have to make the zero into ten instead of borrowing from zero which is not intuitive because it can’t really borrow from zero I borrowed from this 50 and I made that into 49. Let’s do one more problem. If I have 2. 64–0.00486 so once again let’s line up the decimals points, 2.64 – 0.00486. Line up the decimal points at the zeroes on top. We’re going to have a zero here so I have to borrow from to ten. I can’t borrow from the zero so I have to borrow from this entire 40 forty so this 40 becomes a 39. I think I'm running out of space so ten is larger than six, nine is larger than eight, three is not larger than four so this three I'm going to have to borrow so three becomes a thirteen. I apologize for being squinch but the six becomes a five. This is really bad I should do it so messy. But now ten is larger than six, nine is larger than the eight, thus thirteen should be on top on that three thirteen is larger than four and five is larger than zero. We are ready to subtract ten minus six is four, nine minus eight is one, thirteen minus four is nine, five minus zero is five, two minus nothing is two, bring down the decimal point so 2.64–0.00486=2. 5914. I hope I did not confuse you too much but I think you're ready now to try the subtraction of decimals. Have fun.