Alternate mental subtraction method

How I subtract in my head

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.