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 nine thousand four hundred fifty-six minus seven thousand five hundred eighty-nine.
So the way I do this in my head.
I say that nine thousand four hundred fifty-six minus seven thousand five hundred eighty-nine-- you have to
remember the two numbers.
So the first thing I do is I say, well, what's nine thousand four hundred fifty-six
minus just seven thousand?
That's pretty easy because I just take nine thousand minus seven thousand.
So what I can do is I'll cross out this and I'll
subtract seven thousand from it.
And I'm going to get two thousand four hundred fifty six.
So in my head I tell myself that nine thousand four hundred fifty-six minus seven thousand five hundred eighty-nine is the
same thing as-- if I just subtract out the seven thousand--
as two thousand four hundred fifty-six minus five hundred eighty-nine.
I took the seven thousand out of the picture.
I essentially subtracted it from both of these numbers.
Now, if I want to do two thousand four hundred fifty-six minus five hundred eighty-nine what I do is I
subtract five hundred from both of these numbers.
So if I subtract five hundred from this bottom number,
this five will go away.
And if I subtract five hundred from this top number, what happens?
What's two thousand four hundred fifty-six minus five hundred?
Or an easier way to think about it?
What's twenty-four minus five?
Well, that's nineteen.
So it's going to be one thousand nine hundred fifty-six.
Let me scroll up a little bit.
So it's one thousand nine hundred fifty six.
So my original problem has now been reduced to one thousand nine hundred fifty-six minus eighty-nine.
Now I can subtract eighty from both that number and that number.
So if I subtract eighty from this bottom number the eight disappears.
Eighty-nine minus eighty is just nine.
And I subtract eighty from this top number, I can just think of,
well, what's one hundred ninety-five minus eight?
Well, one hundred ninety-five minus eight, let's see.
Fifteen minus eight is seventeen.
So one hundred ninety-five minus eight is going to be one hundred eighty-seven and then you
still have the six there.
So essentially I said, one thousand nine hundred fifty-six minus eighty is one thousand eight hundred seventy-six.
And now my problem has been reduced to one thousand eight hundred seventy-six minus nine.
And then we can do that in our head.
What's seventy-six minus nine?
That's what?
Sixty-seven.
So our final answer is one thousand eight hundred sixty-seven.
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.
Nine thousand four hundred fifty-six minus seven thousand five hundred eighty-nine.
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.
Six is definitely not larger than nine, so I have to borrow.
So I'll borrow ten or I'll borrow one from the tens place,
which ends up being ten.
So the six becomes a sixteen and then the five becomes a four.
Then I go to the tens place.
Four needs to be larger than eight, so let me borrow one
from the hundreds place.
So then that four becomes a fourteen or fourteen tens because
we're in the tens place.
And then this four becomes a three.
Now these two columns or places look good, but right here I
have a three, which is less than a five.
Not cool, so I have to borrow again.
That three becomes a thirteen and then that nine becomes an eight.
And now I'm ready to subtract.
So you get sixteen minus nine is seven.
Fourteen minus eight is six.
Thirteen minus five is eight.
Eight minus seven is one.
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.