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## Arithmetic (all content)

### Unit 2: Lesson 19

Addition and subtraction greater than 1000- Relate place value to standard algorithm for multi-digit addition
- Multi-digit addition with regrouping
- Multi-digit subtraction with regrouping: 6798-3359
- Multi-digit subtraction with regrouping: 7329-6278
- Multi-digit subtraction with regrouping twice
- Alternate mental subtraction method
- Adding multi-digit numbers: 48,029+233,930
- Multi-digit addition
- Relate place value to standard algorithm for multi-digit subtraction
- Multi-digit subtraction: 389,002-76,151
- Multi-digit subtraction

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# Alternate mental subtraction method

Sal explains how he subtracts numbers like 9456 and 7589 in his head. Created by Sal Khan.

## Video transcript

I want to show you a way that,
at least, I find more useful to subtract numbers in my head. And I do it this way-- it's
not necessarily faster on paper, but it allows you to
remember what you're doing. Because if you start borrowing
and stuff it becomes very hard to remember what's
actually going on. So let's try out a
couple of problems. Let's have 9,456 minus 7,589. So the way I do
this in my head. I say that 9,456 minus
7,589-- you have to remember the two numbers. So the first thing I do is
I say, well, what's 9,456 minus is just 7,000? That's pretty easy because I
just take 9,000 minus 7,000. So what I can do is I'll
cross out this and I'll subtract 7,000 from it. And I'm going to get 2,456. So in my head I tell myself
that 9,456 minus 7,589 is the same thing as-- if I just
subtract out the 7,000-- as 2,456 minus 589. I took the 7,000 out
of the picture. I essentially subtracted it
from both of these numbers. Now, if I want to do 2,456
minus 589 what I do is I subtract 500 from both
of these numbers. So if I subtract 500 from
this bottom number, this 5 will go away. And if I subtract 500 from this
top number, what happens? What's 2,456 minus 500? Or an easier way to
think about it? What's 24 minus 5? Well, that's 19. So it's going to be 1,956. Let me scroll up a little bit. So it's 1,956. So my original problem has now
been reduced to 1,956 minus 89. Now I can subtract 80 from both
that number and that number. So if I subtract 80 from this
bottom number the 8 disappears. 898 minus 80 is just 9. And I subtract 80 from this top
number, I can just think of, well, what's 195 minus 8? Well, 195 minus 8, let's see. 15 minus 8 is 17. So 195 minus 8 is going
to be 187 and then you still have the 6 there. So essentially I said,
1,956 minus 80 is 1,876. And now my problem has been
reduced to 1,876 minus 9. And then we can do
that in our head. What's 76 minus 9? That's what? 67. So our final answer is 1,867. And as you can see this isn't
necessarily faster than the way we've done it in other videos. But the reason why I like it
is that at any stage, I just have to remember two numbers. I have to remember my
new top number and my new bottom number. My new bottom number is always
just some of the leftover digits of the original
bottom number. So that's how I like to
do things in my head. Now, just to make sure that we
got the right answer and maybe to compare and contrast
a little bit. Let's do it the
traditional way. 9,456 minus 7,589. So the standard way of doing
it, I like to do all my borrowing before I do any of my
subtraction so that I can stay in my borrowing mode, or you
can think of it as regrouping. So I look at all of my numbers
on top and see, are they all larger than the numbers
on the bottom? And I start here at the right. 6 is definitely not larger
than 9, so I have to borrow. So I'll borrow 10 or I'll
borrow 1 from the 10's place, which ends up being 10. So the 6 becomes a 16 and
then the 5 becomes a 4. Then I go to the 10's place. 4 needs to be larger than
8, so let me borrow 1 from the 100's place. So then that 4 becomes a 14
or fourteen 10's because we're in the 10's place. And then this 4 becomes a 3. Now these two columns or places
look good, but right here I have a 3, which is
less than a 5. Not cool, so I have
to borrow again. That 3 becomes a 13 and
then that 9 becomes an 8. And now I'm ready to subtract. So you get 16 minus 9 is 7. 14 minus 8 is 16. 13 minus 5 is 8. 8 minus 7 is 1. And lucky for us, we
got the right answer. I want to make it very clear. There's no better
way to do this. This way is actually kind of
longer and it takes up more space on your paper than this
way was, but this for me, is very hard to remember. It's very hard for me to keep
track of what I borrowed and what the other number
is and et cetera. But here, at any point
in time, I just have to remember two numbers. And the two numbers get
simpler every step that I go through this process. So this is why I think
that this is a little bit easier in my head. But this might be, depending on
the context, easier on paper. But at least here you didn't
have to borrow or regroup. Well, hopefully you find
that a little bit useful.