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Welcome to the presentation on subtracting decimal numbers. Let's get started with some problems. The first problem I have here says 5.73 minus 0.0821 equals who knows? So the first thing you always want to do with a decimal like this, and I actually kind of inadvertently did this, is that you want to line up the decimals. so you actually want this decimal to be right above this decimal. I almost did that 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, and I'll put the decimal here. 0.0821. And some people say it's good to always put a zero in front of the decimal. My wife's a doctor and she says it's critical otherwise you might give someone the wrong amount of medicine. 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 decimals is we're going to have to subtract this 21 ten-thousandths or this 2 and this 1 from something. We can't just subtract it from this blank space. So we have to add two 0s here. And as you know, with the decimal when you add 0s to the end of it, it really doesn't change the value of the decimal. So at this point, we just view this like a level four subtraction problem. So the first thing we do in any subtraction problem 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 this 0 is less than this 1, this 0 is less than this 2, this 3 is less than this 8. So we're going to have to borrow. Some people will like to do their borrowing and subtracting, they kind of alternate between the two. I like to do all of my borrowing ahead of time. So what I do is I start in the top right and I say OK, 0 is less than 1. So that 0 becomes a 10. But in order to become a 10 I would have had to borrow 1 from some place. I look to the left of that 0 and I say well, can I borrow the 1 from 0? Well, no. This is just the way I do it. There are people who would actually let you borrow the 1 from the 0, but I say no, instead of borrowing the 1 from the 0, I borrow the 1 from this entire 30. So this 30 -- see, there's a 30 so I'm going to borrow 1 from it and it becomes 29. So we borrowed 1 from this 30 to get a 10 here, and now let's check again to see if all of our numbers on top are larger than all the numbers on the bottom. Well 10 is larger than 1, 9 is larger than 2, 2 is not larger than 8. So we have to borrow again. So if we're going to borrow, the 2 becomes a 12, and the 7 -- we borrowed 1 from that -- becomes a 6. So let's check again. 10 is larger than 1, 9 is larger than 2, 12 is larger than 8, 6 is larger than 0, and 5 is larger than 0. So now we've done all of our borrowing and we're ready to do some subtraction, and this is the easy part. 10 minus 1 is 9. 9 minus 2 is 7. 12 minus 8 is 4. 6 minus 0 is 6. 5 minus 0 is 5. And we just bring down the decimal point. So there's our answer. 5.73 minus 0.0821 is equal to 5.6479. There you go. I probably confused you, so let's do some more problems. Here's another one. 8 -- let me leave some space on top to do the borrowing -- 8.25 minus 0.0105. So what was that first step that I always have to do? Right. To line up the decimals. So let me do that. So it's 8.25 and 0.0105. Notice I lined up this decimal right below this decimal. Now I add the 0s, just because this 0 and this 5 need to be subtracted from something. Now let me do my borrowing. So once again, all I do is check to see whether the top number is larger than the number below it. Well, this 0 is smaller than 5, so I'm going to have to borrow. So I'm going to borrow. I can't borrow from this 0, I have to borrow from this entire 50. So this 50, if I borrow 1 from 50 I get 49. And this 0 will then become a 10, right? I borrowed 1 from 50 to get a 10. Now, am I done? 10 is larger than 5. 9 is larger than 0. 4 is larger than 1. 2 is larger than 0. 8 is larger than 0. So I think I'm ready to subtract. 10 minus 5, well that's 5. 9 minus 0 is 9. 4 minus 1 is 3. 2 minus 0 is 2. 8 minus 0 is 8. And I bring down the decimal point. So if you mastered level four subtraction, the decimal problems really are just about lining up the decimal point, adding the 0s and then just doing a normal subtraction 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 in a lot of schools. A lot of schools they'll do the subtraction and they'll borrow alternatively. But I find this easier when I just borrow ahead of time, and I also, like for example in this problem, when I had to make this 0 into a 10, instead of borrowing from the 0, which is not intuitive because I can't really borrow from the 0, I borrowed from this entire 50 and I made that into a 49. Let's do one more problem. If I have 2.64 minus 0.0486. So once again, let's line up the decimal points. 2.64 and it's .0486. Lined up the decimal points, the 0s on top. You're going to have a 0 here, so I have to borrow. Becomes a 10. Can't borrow from the 0, so I have to borrow from this entire 40. So this 40 becomes a 39. I think I'm running out of space. So 10 is larger than 6. 9 is larger than 8. 3 is not larger than 4. So this 3 I'm going to have to borrow. So 3 becomes a 13. I apologize, I'm becoming scrunched. And this 6 becomes a 5. This is really bad, I shouldn't do it so messy. But now we say the 10 is larger than 6, the 9 is larger than the 8, this 13, this 13 should be on top of that 3. The 13 is larger than 4, and 5 is larger than 0. So we're ready to subtract. 10 minus 6 is 4. 9 minus 8 is 1. 13 minus 4 is 9. 5 minus 0 is 5. 2 minus nothing is 2. Bring down the decimal point. So 2.64 minus 0.0486 is equal to 2.5914. Hope I didn't confuse you too much. But I think you're ready now to try the subtraction of decimals. Have fun.