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I want to show you a way that, at least, I find more useful to

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subtract numbers in my head.

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And I do it this way-- it's not necessarily faster on

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paper, but it allows you to remember what you're doing.

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Because if you start borrowing and stuff it becomes very hard

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to remember what's actually going on.

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So let's try out a couple of problems.

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Let's have 9,456 minus 7,589.

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So the way I do this in my head.

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I say that 9,456 minus 7,589-- you have to

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remember the two numbers.

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So the first thing I do is I say, well, what's 9,456

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minus is just 7,000?

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That's pretty easy because I just take 9,000 minus 7,000.

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So what I can do is I'll cross out this and I'll

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subtract 7,000 from it.

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And I'm going to get 2,456.

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So in my head I tell myself that 9,456 minus 7,589 is the

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same thing as-- if I just subtract out the 7,000--

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as 2,456 minus 589.

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I took the 7,000 out of the picture.

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I essentially subtracted it from both of these numbers.

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Now, if I want to do 2,456 minus 589 what I do is I

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subtract 500 from both of these numbers.

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So if I subtract 500 from this bottom number,

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this 5 will go away.

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And if I subtract 500 from this top number, what happens?

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What's 2,456 minus 500?

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Or an easier way to think about it?

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What's 24 minus 5?

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Well, that's 19.

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So it's going to be 1,956.

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Let me scroll up a little bit.

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So it's 1,956.

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So my original problem has now been reduced to 1,956 minus 89.

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Now I can subtract 80 from both that number and that number.

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So if I subtract 80 from this bottom number the 8 disappears.

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898 minus 80 is just 9.

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And I subtract 80 from this top number, I can just think of,

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well, what's 195 minus 8?

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Well, 195 minus 8, let's see.

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15 minus 8 is 17.

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So 195 minus 8 is going to be 187 and then you

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still have the 6 there.

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So essentially I said, 1,956 minus 80 is 1,876.

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And now my problem has been reduced to 1,876 minus 9.

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And then we can do that in our head.

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What's 76 minus 9?

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That's what?

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67.

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So our final answer is 1,867.

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And as you can see this isn't necessarily faster than the way

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we've done it in other videos.

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But the reason why I like it is that at any stage, I just

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have to remember two numbers.

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I have to remember my new top number and my

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new bottom number.

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My new bottom number is always just some of the leftover

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digits of the original bottom number.

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So that's how I like to do things in my head.

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Now, just to make sure that we got the right answer and maybe

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to compare and contrast a little bit.

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Let's do it the traditional way.

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9,456 minus 7,589.

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So the standard way of doing it, I like to do all my

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borrowing before I do any of my subtraction so that I can stay

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in my borrowing mode, or you can think of it as regrouping.

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So I look at all of my numbers on top and see, are they all

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larger than the numbers on the bottom?

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And I start here at the right.

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6 is definitely not larger than 9, so I have to borrow.

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So I'll borrow 10 or I'll borrow 1 from the 10's place,

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which ends up being 10.

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So the 6 becomes a 16 and then the 5 becomes a 4.

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Then I go to the 10's place.

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4 needs to be larger than 8, so let me borrow 1

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from the 100's place.

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So then that 4 becomes a 14 or fourteen 10's because

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we're in the 10's place.

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And then this 4 becomes a 3.

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Now these two columns or places look good, but right here I

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have a 3, which is less than a 5.

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Not cool, so I have to borrow again.

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That 3 becomes a 13 and then that 9 becomes an 8.

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And now I'm ready to subtract.

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So you get 16 minus 9 is 7.

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14 minus 8 is 16.

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13 minus 5 is 8.

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8 minus 7 is 1.

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And lucky for us, we got the right answer.

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I want to make it very clear.

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There's no better way to do this.

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This way is actually kind of longer and it takes up more

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space on your paper than this way was, but this for me,

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is very hard to remember.

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It's very hard for me to keep track of what I borrowed and

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what the other number is and et cetera.

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But here, at any point in time, I just have to

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remember two numbers.

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And the two numbers get simpler every step that I

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go through this process.

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So this is why I think that this is a little

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bit easier in my head.

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But this might be, depending on the context, easier on paper.

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But at least here you didn't have to borrow or regroup.

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Well, hopefully you find that a little bit useful.