WEBVTT 00:00:00.467 --> 00:00:03.509 I want to show you a way that, at least, I find more useful to 00:00:04.428 --> 00:00:05.346 subtract numbers in my head. 00:00:05.346 --> 00:00:07.916 And I do it this way-- it's not necessarily faster on 00:00:07.931 --> 00:00:10.668 paper, but it allows you to remember what you're doing. 00:00:10.668 --> 00:00:12.724 Because if you start borrowing and stuff it becomes very hard 00:00:12.724 --> 00:00:14.603 to remember what's actually going on. 00:00:14.603 --> 00:00:16.417 So let's try out a couple of problems. 00:00:16.417 --> 00:00:27.343 Let's have nine thousand four hundred fifty-six minus seven thousand five hundred eighty-nine. 00:00:27.343 --> 00:00:29.686 So the way I do this in my head. 00:00:29.686 --> 00:00:35.092 I say that nine thousand four hundred fifty-six minus seven thousand five hundred eighty-nine-- you have to 00:00:35.092 --> 00:00:36.545 remember the two numbers. 00:00:36.545 --> 00:00:40.874 So the first thing I do is I say, well, what's nine thousand four hundred fifty-six 00:00:40.874 --> 00:00:44.109 minus just seven thousand? 00:00:44.109 --> 00:00:48.134 That's pretty easy because I just take nine thousand minus seven thousand. 00:00:48.134 --> 00:00:51.575 So what I can do is I'll cross out this and I'll 00:00:51.575 --> 00:00:53.652 subtract seven thousand from it. 00:00:53.652 --> 00:00:58.094 And I'm going to get two thousand four hundred fifty six. 00:00:58.094 --> 00:01:05.414 So in my head I tell myself that nine thousand four hundred fifty-six minus seven thousand five hundred eighty-nine is the 00:01:05.414 --> 00:01:08.667 same thing as-- if I just subtract out the seven thousand-- 00:01:08.667 --> 00:01:12.966 as two thousand four hundred fifty-six minus five hundred eighty-nine. 00:01:12.982 --> 00:01:15.178 I took the seven thousand out of the picture. 00:01:15.178 --> 00:01:18.958 I essentially subtracted it from both of these numbers. 00:01:18.958 --> 00:01:25.386 Now, if I want to do two thousand four hundred fifty-six minus five hundred eighty-nine what I do is I 00:01:25.386 --> 00:01:28.818 subtract five hundred from both of these numbers. 00:01:28.818 --> 00:01:31.288 So if I subtract five hundred from this bottom number, 00:01:31.288 --> 00:01:33.163 this five will go away. 00:01:33.163 --> 00:01:36.312 And if I subtract five hundred from this top number, what happens? 00:01:36.312 --> 00:01:39.538 What's two thousand four hundred fifty-six minus five hundred? 00:01:39.538 --> 00:01:41.146 Or an easier way to think about it? 00:01:41.146 --> 00:01:42.947 What's twenty-four minus five? 00:01:42.947 --> 00:01:43.836 Well, that's nineteen. 00:01:43.836 --> 00:01:49.033 So it's going to be one thousand nine hundred fifty-six. 00:01:49.033 --> 00:01:50.791 Let me scroll up a little bit. 00:01:50.791 --> 00:01:52.213 So it's one thousand nine hundred fifty six. 00:01:52.213 --> 00:01:57.510 So my original problem has now been reduced to one thousand nine hundred fifty-six minus eighty-nine. 00:01:57.510 --> 00:02:01.692 Now I can subtract eighty from both that number and that number. 00:02:01.692 --> 00:02:04.741 So if I subtract eighty from this bottom number the eight disappears. 00:02:04.741 --> 00:02:07.102 Eighty-nine minus eighty is just nine. 00:02:07.102 --> 00:02:09.412 And I subtract eighty from this top number, I can just think of, 00:02:09.412 --> 00:02:12.385 well, what's one hundred ninety-five minus eight? 00:02:12.385 --> 00:02:15.157 Well, one hundred ninety-five minus eight, let's see. 00:02:15.157 --> 00:02:17.909 Fifteen minus eight is seventeen. 00:02:17.924 --> 00:02:25.138 So one hundred ninety-five minus eight is going to be one hundred eighty-seven and then you 00:02:25.138 --> 00:02:26.656 still have the six there. 00:02:26.656 --> 00:02:31.910 So essentially I said, one thousand nine hundred fifty-six minus eighty is one thousand eight hundred seventy-six. 00:02:31.910 --> 00:02:35.995 And now my problem has been reduced to one thousand eight hundred seventy-six minus nine. 00:02:35.995 --> 00:02:37.450 And then we can do that in our head. 00:02:37.450 --> 00:02:39.679 What's seventy-six minus nine? 00:02:39.679 --> 00:02:40.363 That's what? 00:02:40.363 --> 00:02:41.660 Sixty-seven. 00:02:41.660 --> 00:02:47.789 So our final answer is one thousand eight hundred sixty-seven. 00:02:47.789 --> 00:02:50.946 And as you can see this isn't necessarily faster than the way 00:02:50.961 --> 00:02:52.500 we've done it in other videos. 00:02:52.500 --> 00:02:54.999 But the reason why I like it is that at any stage, I just 00:02:54.999 --> 00:02:56.465 have to remember two numbers. 00:02:56.465 --> 00:02:58.845 I have to remember my new top number and my 00:02:58.845 --> 00:03:00.067 new bottom number. 00:03:00.067 --> 00:03:03.466 My new bottom number is always just some of the leftover 00:03:03.466 --> 00:03:05.159 digits of the original bottom number. 00:03:05.159 --> 00:03:07.917 So that's how I like to do things in my head. 00:03:07.917 --> 00:03:10.452 Now, just to make sure that we got the right answer and maybe 00:03:10.452 --> 00:03:13.239 to compare and contrast a little bit. 00:03:13.239 --> 00:03:15.190 Let's do it the traditional way. 00:03:15.190 --> 00:03:24.907 Nine thousand four hundred fifty-six minus seven thousand five hundred eighty-nine. 00:03:24.907 --> 00:03:28.467 So the standard way of doing it, I like to do all my 00:03:28.467 --> 00:03:31.313 borrowing before I do any of my subtraction so that I can stay 00:03:31.313 --> 00:03:34.913 in my borrowing mode, or you can think of it as regrouping. 00:03:34.928 --> 00:03:37.793 So I look at all of my numbers on top and see, are they all 00:03:37.793 --> 00:03:39.331 larger than the numbers on the bottom? 00:03:39.331 --> 00:03:40.717 And I start here at the right. 00:03:40.717 --> 00:03:43.583 Six is definitely not larger than nine, so I have to borrow. 00:03:43.583 --> 00:03:46.627 So I'll borrow ten or I'll borrow one from the tens place, 00:03:46.627 --> 00:03:48.134 which ends up being ten. 00:03:48.134 --> 00:03:52.998 So the six becomes a sixteen and then the five becomes a four. 00:03:52.998 --> 00:03:54.269 Then I go to the tens place. 00:03:54.269 --> 00:03:57.840 Four needs to be larger than eight, so let me borrow one 00:03:57.856 --> 00:03:59.570 from the hundreds place. 00:03:59.570 --> 00:04:03.123 So then that four becomes a fourteen or fourteen tens because 00:04:03.123 --> 00:04:04.408 we're in the tens place. 00:04:04.408 --> 00:04:07.168 And then this four becomes a three. 00:04:07.168 --> 00:04:09.897 Now these two columns or places look good, but right here I 00:04:09.897 --> 00:04:12.201 have a three, which is less than a five. 00:04:12.201 --> 00:04:14.396 Not cool, so I have to borrow again. 00:04:14.396 --> 00:04:18.825 That three becomes a thirteen and then that nine becomes an eight. 00:04:18.825 --> 00:04:21.628 And now I'm ready to subtract. 00:04:21.628 --> 00:04:24.499 So you get sixteen minus nine is seven. 00:04:24.499 --> 00:04:27.334 Fourteen minus eight is six. 00:04:27.334 --> 00:04:29.445 Thirteen minus five is eight. 00:04:29.445 --> 00:04:31.087 Eight minus seven is one. 00:04:31.087 --> 00:04:33.907 And lucky for us, we got the right answer. 00:04:33.907 --> 00:04:34.684 I want to make it very clear. 00:04:34.684 --> 00:04:36.534 There's no better way to do this. 00:04:36.534 --> 00:04:39.678 This way is actually kind of longer and it takes up more 00:04:39.678 --> 00:04:43.123 space on your paper than this way was, but this for me, 00:04:43.123 --> 00:04:44.586 is very hard to remember. 00:04:44.586 --> 00:04:47.480 It's very hard for me to keep track of what I borrowed and 00:04:47.480 --> 00:04:50.038 what the other number is and et cetera. 00:04:50.038 --> 00:04:52.049 But here, at any point in time, I just have to 00:04:52.049 --> 00:04:53.715 remember two numbers. 00:04:53.715 --> 00:04:56.645 And the two numbers get simpler every step that I 00:04:56.645 --> 00:04:58.655 go through this process. 00:04:58.655 --> 00:05:00.048 So this is why I think that this is a little 00:05:00.048 --> 00:05:01.437 bit easier in my head. 00:05:01.437 --> 00:05:03.860 But this might be, depending on the context, easier on paper. 00:05:03.860 --> 00:05:06.587 But at least here you didn't have to borrow or regroup. 00:05:06.587 --> 00:05:21.118 Well, hopefully you find that a little bit useful.