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Welcome to the presentation on subtracting decimal numbers.

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Let's get started with some problems.

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The first problem I have here says 5.73 minus

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0.0821 equals who knows?

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So the first thing you always want to do with a decimal like

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this, and I actually kind of inadvertently did this, is that

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you want to line up the decimals.

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so you actually want this decimal to be right

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above this decimal.

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I almost did that when I did it, it must have been my

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subconscious doing it.

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But let me just do it a little bit neater.

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So it's 5.73, and I'll put the decimal here.

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0.0821.

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And some people say it's good to always put a zero in

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front of the decimal.

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My wife's a doctor and she says it's critical otherwise

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you might give someone the wrong amount of medicine.

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So, we've lined up the decimals and now we're

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ready to subtract.

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So one thing that you have to think about when you do

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decimals is we're going to have to subtract this 21

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ten-thousandths or this 2 and this 1 from something.

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We can't just subtract it from this blank space.

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So we have to add two 0s here.

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And as you know, with the decimal when you add 0s to the

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end of it, it really doesn't change the value

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of the decimal.

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So at this point, we just view this like a level

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four subtraction problem.

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So the first thing we do in any subtraction problem is see if

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any of the numbers on top are smaller than any of the

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numbers on the bottom.

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Well in this case there are a lot of them.

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So this 0 is less than this 1, this 0 is less than this 2,

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this 3 is less than this 8.

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So we're going to have to borrow.

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Some people will like to do their borrowing and

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subtracting, they kind of alternate between the two.

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I like to do all of my borrowing ahead of time.

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So what I do is I start in the top right and I say

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OK, 0 is less than 1.

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So that 0 becomes a 10.

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But in order to become a 10 I would have had to

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borrow 1 from some place.

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I look to the left of that 0 and I say well, can

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I borrow the 1 from 0?

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Well, no.

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This is just the way I do it.

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There are people who would actually let you borrow the 1

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from the 0, but I say no, instead of borrowing the 1

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from the 0, I borrow the 1 from this entire 30.

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So this 30 -- see, there's a 30 so I'm going to borrow 1

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from it and it becomes 29.

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So we borrowed 1 from this 30 to get a 10 here, and now let's

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check again to see if all of our numbers on top are larger

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than all the numbers on the bottom.

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Well 10 is larger than 1, 9 is larger than 2, 2

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is not larger than 8.

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So we have to borrow again.

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So if we're going to borrow, the 2 becomes a 12, and the 7

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-- we borrowed 1 from that -- becomes a 6.

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So let's check again.

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10 is larger than 1, 9 is larger than 2, 12 is larger

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than 8, 6 is larger than 0, and 5 is larger than 0.

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So now we've done all of our borrowing and we're ready to

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do some subtraction, and this is the easy part.

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10 minus 1 is 9.

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9 minus 2 is 7.

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12 minus 8 is 4.

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6 minus 0 is 6.

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5 minus 0 is 5.

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And we just bring down the decimal point.

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So there's our answer.

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5.73 minus 0.0821 is equal to 5.6479.

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There you go.

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I probably confused you, so let's do some more problems.

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Here's another one.

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8 -- let me leave some space on top to do the borrowing

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-- 8.25 minus 0.0105.

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So what was that first step that I always have to do?

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Right.

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To line up the decimals.

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So let me do that.

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So it's 8.25 and 0.0105.

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Notice I lined up this decimal right below this decimal.

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Now I add the 0s, just because this 0 and this 5 need to be

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subtracted from something.

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Now let me do my borrowing.

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So once again, all I do is check to see whether the

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top number is larger than the number below it.

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Well, this 0 is smaller than 5, so I'm going to have to borrow.

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So I'm going to borrow.

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I can't borrow from this 0, I have to borrow

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from this entire 50.

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So this 50, if I borrow 1 from 50 I get 49.

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And this 0 will then become a 10, right?

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I borrowed 1 from 50 to get a 10.

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Now, am I done?

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10 is larger than 5.

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9 is larger than 0.

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4 is larger than 1.

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2 is larger than 0.

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8 is larger than 0.

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So I think I'm ready to subtract.

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10 minus 5, well that's 5.

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9 minus 0 is 9.

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4 minus 1 is 3.

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2 minus 0 is 2.

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8 minus 0 is 8.

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And I bring down the decimal point.

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So if you mastered level four subtraction, the decimal

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problems really are just about lining up the decimal point,

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adding the 0s and then just doing a normal

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subtraction problem.

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In general with subtraction I think most people have the most

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trouble with the borrowing.

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The way I do it I think is a little bit different than is

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taught in a lot of schools.

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A lot of schools they'll do the subtraction and they'll

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borrow alternatively.

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But I find this easier when I just borrow ahead of time, and

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I also, like for example in this problem, when I had to

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make this 0 into a 10, instead of borrowing from the 0, which

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is not intuitive because I can't really borrow from the 0,

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I borrowed from this entire 50 and I made that into a 49.

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Let's do one more problem.

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If I have 2.64 minus 0.0486.

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So once again, let's line up the decimal points.

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2.64 and it's .0486.

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Lined up the decimal points, the 0s on top.

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You're going to have a 0 here, so I have to borrow.

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Becomes a 10.

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Can't borrow from the 0, so I have to borrow

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from this entire 40.

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So this 40 becomes a 39.

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I think I'm running out of space.

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So 10 is larger than 6.

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9 is larger than 8.

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3 is not larger than 4.

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So this 3 I'm going to have to borrow.

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So 3 becomes a 13.

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I apologize, I'm becoming scrunched.

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And this 6 becomes a 5.

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This is really bad, I shouldn't do it so messy.

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But now we say the 10 is larger than 6, the 9 is larger than

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the 8, this 13, this 13 should be on top of that 3.

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The 13 is larger than 4, and 5 is larger than 0.

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So we're ready to subtract.

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10 minus 6 is 4.

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9 minus 8 is 1.

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13 minus 4 is 9.

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5 minus 0 is 5.

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2 minus nothing is 2.

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Bring down the decimal point.

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So 2.64 minus 0.0486 is equal to 2.5914.

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Hope I didn't confuse you too much.

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But I think you're ready now to try the

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subtraction of decimals.

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Have fun.

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