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# Subtracting decimals (old)

Video transcript

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.