0:00:00.530,0:00:01.674 If you've practiced 0:00:01.674,0:00:04.729 and hopefully, memorized your multiplication tables, 0:00:04.729,0:00:08.785 you'll now find out that you're prepared to do most any multiplication problem. 0:00:08.785,0:00:11.058 You just have to understand, 0:00:11.058,0:00:12.699 I guess for lack of a better word, 0:00:12.699,0:00:14.340 the system of how to do it. 0:00:14.350,0:00:15.836 But we're not just going to teach you the system, 0:00:15.836,0:00:17.760 we're going to show you why it works. 0:00:17.760,0:00:20.280 So let's start with a multiplication problem 0:00:20.280,0:00:23.420 that you probably think that you don't know how to do. 0:00:23.420,0:00:30.119 Let's do sixteen times nine. 0:00:30.119,0:00:31.865 Sixteen times nine. 0:00:31.865,0:00:32.858 And you immediately might say, 0:00:32.858,0:00:36.004 Sal, I haven't memorized my sixteen times tables, 0:00:36.004,0:00:38.790 there's no way I'm going to be able to do that problem. 0:00:38.790,0:00:41.214 And my answer to you is, you can absolutely do it 0:00:41.214,0:00:43.294 because we can break it down into problems 0:00:43.294,0:00:45.262 that you do know the answer to. 0:00:45.262,0:00:46.532 The way you do this one 0:00:46.532,0:00:49.710 is first multiply nine times the ones place here. 0:00:49.710,0:00:52.240 So you multiply nine times six. 0:00:52.250,0:00:54.820 And I think you know what nine times six is. 0:00:54.820,0:00:56.760 I'll write it down here. 0:00:56.770,0:01:01.090 So nine times six is fifty-four. 0:01:01.100,0:01:03.380 You know that from your multiplication tables. 0:01:03.380,0:01:05.861 And so what you do is you write fifty-four, 0:01:05.861,0:01:08.975 but you only write the four down here in the ones place, 0:01:08.975,0:01:11.935 and you carry the five. 0:01:11.935,0:01:13.710 That's exactly what you're doing. 0:01:13.710,0:01:17.004 We also use word carry when you add 0:01:17.004,0:01:19.755 and you kind of have an extra five to deal with, 0:01:19.755,0:01:21.113 but let's just call that carrying. 0:01:21.128,0:01:24.113 For lack of better words. 0:01:24.113,0:01:28.429 Now, we then multiply nine times one. 0:01:28.429,0:01:29.329 Nine times one. 0:01:29.329,0:01:31.158 Well, that's straightforward. 0:01:31.158,0:01:33.490 Nine times one is equal to nine. 0:01:33.500,0:01:35.650 Anything times one is equal to itself. 0:01:35.650,0:01:38.670 But we have this five sitting up here, so nine times one, 0:01:38.680,0:01:40.740 we have to add that five. 0:01:40.750,0:01:45.144 So we have to add that plus five. 0:01:45.144,0:01:47.102 And so what do we get? 0:01:47.102,0:01:50.160 So nine times one plus five 0:01:50.160,0:01:55.638 is nine plus five, which is fourteen. 0:01:55.638,0:01:57.702 Let me write it right there. 0:01:57.702,0:01:59.689 Fourteen. 0:01:59.689,0:02:00.590 And there you have it. 0:02:00.590,0:02:04.180 Sixteen times nine is one hundred forty-four. 0:02:04.180,0:02:06.534 And if you remembered your times tables up to twelve 0:02:06.534,0:02:08.440 you also realize that's twelve times twelve. 0:02:08.440,0:02:12.260 But just knowing only these two pieces of information, 0:02:12.260,0:02:14.655 we were able to solve a harder problem. 0:02:14.655,0:02:17.499 Now you might say, Okay Sal, that's a neat little trick you just did, 0:02:17.499,0:02:19.220 but how does it work? 0:02:19.220,0:02:20.540 And you should always ask that. 0:02:20.550,0:02:22.160 You shouldn't just take it-- 0:02:22.160,0:02:25.150 you shouldn't just memorize the system and assume that it works. 0:02:25.150,0:02:27.920 And to explain that I'm just going to rewrite these numbers. 0:02:27.930,0:02:32.870 I can rewrite sixteen as ten-- let me do it right here. 0:02:32.870,0:02:34.980 Ten plus six. 0:02:34.990,0:02:36.930 This is sixteen. 0:02:36.930,0:02:37.865 And I can rewrite nine, 0:02:37.865,0:02:40.760 well, I'm just going to write nine as nine. Right there. 0:02:40.770,0:02:44.190 And now let me do the multiplication problem. 0:02:44.190,0:02:46.960 I'll put a little multiplication sign out there. 0:02:46.960,0:02:50.830 So first I want to multiply the nine times the six. 0:02:50.840,0:02:52.810 And you might say, hey Sal, why did you divide it this way? 0:02:52.810,0:02:56.490 Well, I wanted to separate the ones place from the tens place. 0:02:56.500,0:02:59.580 This one here that's in the second column, 0:02:59.590,0:03:00.990 it isn't a one, it's a ten. 0:03:00.990,0:03:02.880 It's a ten plus a six, 0:03:02.880,0:03:04.390 so that's why I wanted to write it that way. 0:03:04.400,0:03:06.050 But anyway, let's do this problem. 0:03:06.060,0:03:08.310 So we do it the exact same way we did it before. 0:03:08.310,0:03:10.707 We say nine times six-- 0:03:10.707,0:03:11.838 let me write that down. 0:03:11.838,0:03:15.400 Nine times six is equal to fifty-four. 0:03:15.400,0:03:16.528 But instead of writing fifty-four, 0:03:16.528,0:03:21.740 I'm going to write that's equal to fifty plus four. 0:03:21.750,0:03:25.060 Nine times six is equal to fifty plus four. 0:03:25.060,0:03:27.270 Well, this is my ones column right here. 0:03:27.280,0:03:29.340 Let me make a little dotted line. 0:03:29.340,0:03:30.580 This is my ones column. 0:03:30.590,0:03:32.847 So I can only put a four down here, 0:03:32.847,0:03:35.410 but I need something to do with the fifty. 0:03:35.410,0:03:36.773 I have to put it some place 0:03:36.773,0:03:39.537 and just the convention or at least the way that I've learned it, 0:03:39.537,0:03:40.685 you put the fifty up here. 0:03:40.685,0:03:42.166 I could've put the fifty down here too, 0:03:42.166,0:03:46.730 as long as we remember that this fifty now goes into this column. 0:03:46.740,0:03:48.330 So you can stick the fifty over here. 0:03:48.340,0:03:50.470 That's what we did in the first video. 0:03:50.470,0:03:52.370 I just wrote a five. 0:03:52.380,0:03:55.854 In that first video, I just put a five here 0:03:55.854,0:03:57.830 because that was in the tens place. 0:03:57.840,0:03:59.827 A five here really means fifty. 0:03:59.827,0:04:01.710 A one here really means ten. 0:04:01.710,0:04:03.479 But now I'm writing it out, 0:04:03.479,0:04:06.620 so you can see that they really mean fifty and ten. 0:04:06.620,0:04:09.952 And then you say, what's nine times ten? 0:04:09.952,0:04:14.853 Nine times ten. 0:04:14.853,0:04:16.278 Well, you've memorized this. 0:04:16.278,0:04:18.860 And anything times ten is just that anything with a zero. 0:04:18.870,0:04:20.430 So it's ninety. 0:04:20.430,0:04:22.831 So it's nine times ten is ninety, 0:04:22.831,0:04:25.043 and then we want to add fifty to it. 0:04:25.043,0:04:26.860 So we want to add fifty to it. 0:04:26.870,0:04:28.709 What's ninety plus fifty? 0:04:28.709,0:04:33.850 It is one hundred forty. 0:04:33.850,0:04:35.850 So nine times ten is ninety, 0:04:35.850,0:04:39.010 plus fifty is one hundred forty. 0:04:39.010,0:04:40.543 And we could rewrite one hundred forty 0:04:40.543,0:04:45.620 as one hundred plus forty just to be consistent. 0:04:45.620,0:04:50.553 So what we'll do is we'll put the forty down here, 0:04:50.553,0:04:51.872 and then we carry the one hundred, 0:04:51.872,0:04:53.406 but the one hundred really doesn't go anywhere. 0:04:53.406,0:04:54.925 I mean we could write it up here. 0:04:54.925,0:04:57.342 We could put it-- 0:04:57.342,0:04:58.882 Well, we could write the one hundred over here. 0:04:58.882,0:05:00.250 We could put it over here. 0:05:00.250,0:05:02.180 There's a bunch of different places we could put the one hundred, 0:05:02.190,0:05:06.125 but the important thing is that it sticks out into this next column 0:05:06.125,0:05:07.230 that I haven't drawn yet. 0:05:07.240,0:05:09.020 So then you'll put one hundred here. 0:05:09.020,0:05:13.207 So our answer is one hundred plus forty plus four, 0:05:13.207,0:05:16.154 which is one hundred forty-four. 0:05:16.154,0:05:19.440 Hopefully you found that reasonably explanatory. 0:05:19.450,0:05:22.001 Let's try a couple of other problems, 0:05:22.001,0:05:24.860 because I think it's all about seeing examples. 0:05:24.870,0:05:35.155 So let's try fifty-five times eight. 0:05:35.155,0:05:37.774 Fifty-five times eight. 0:05:37.774,0:05:39.255 Same exercise. 0:05:39.255,0:05:40.510 First, you start with the eight. 0:05:40.510,0:05:41.800 Eight times five. 0:05:41.800,0:05:42.820 Let me write it down. 0:05:42.820,0:05:47.130 Eight times five we know is forty. 0:05:47.140,0:05:49.950 So eight times five, you write the zero down here. 0:05:49.950,0:05:52.840 It's zero plus forty. 0:05:52.850,0:05:54.820 And then you say eight times five again. 0:05:54.820,0:05:56.000 That's forty. 0:05:56.010,0:05:59.560 But then you add the four to here, so you get forty-four. 0:05:59.560,0:06:02.100 So it's four hundred forty. 0:06:02.110,0:06:04.184 And you can try to do it the same way I did that last one 0:06:04.184,0:06:07.170 where I broke it out into fifty plus five and then an eight. 0:06:07.180,0:06:08.183 But I think with more examples, 0:06:08.183,0:06:11.910 you'll see this will all become a bit of second nature to you. 0:06:11.920,0:06:14.714 So let me do another one in this-- 0:06:14.714,0:06:18.830 let me do it in this salmon. This light red, salmon color. 0:06:18.830,0:06:27.260 So let's say I had seventy-eight times-- let's do it times seven. 0:06:27.270,0:06:28.950 Eight times seven. 0:06:28.950,0:06:31.240 Eight times seven is fifty-six. 0:06:31.250,0:06:33.050 Let me write it-- this is a different problem now. 0:06:33.050,0:06:36.550 So eight times seven is equal to fifty-six. 0:06:36.550,0:06:40.470 We write the six down here, put the five up there. 0:06:40.470,0:06:43.590 Seven times seven is forty-nine. 0:06:43.600,0:06:46.540 Seven times seven is equal to forty-nine. 0:06:46.550,0:06:49.750 But we have to add this five up here, so you add this five. 0:06:49.750,0:06:52.045 What's forty-nine plus five? 0:06:52.045,0:06:53.480 Well, that's fifty-four. 0:06:53.490,0:06:55.580 So seven times seven is forty-nine. 0:06:55.580,0:06:57.960 Plus five is fifty-four. 0:06:57.970,0:07:01.790 Five hundred forty-six. 0:07:01.800,0:07:02.562 Ten minutes ago, 0:07:02.562,0:07:06.175 you probably never thought that you could figure out the seventy-eight multiplication tables, 0:07:06.175,0:07:08.190 but you see it's a pretty straightforward process. 0:07:08.190,0:07:09.680 Let's do a bunch more. 0:07:09.680,0:07:13.810 I'm just going to do these until we all just collapse. 0:07:13.820,0:07:16.804 Collapse from multiplication fatigue. 0:07:16.804,0:07:25.865 Let's do an eighty-nine times-- let's do it times three. 0:07:25.865,0:07:27.600 What's three times nine? 0:07:27.600,0:07:31.390 Three times nine is equal to twenty-seven. 0:07:31.390,0:07:33.070 Put the seven in the ones place. 0:07:33.080,0:07:35.287 Put the two up here in the tens place, 0:07:35.287,0:07:36.847 because it's twenty plus seven. 0:07:36.847,0:07:38.360 Two tens is twenty. 0:07:38.370,0:07:40.330 Plus seven is twenty-seven. 0:07:40.330,0:07:42.950 And then three times eight is twenty-four. 0:07:42.950,0:07:46.240 Three times eight is equal to twenty-four. 0:07:46.250,0:07:47.535 But I have this two sitting up here 0:07:47.535,0:07:49.120 so I'm going to have to add a two. 0:07:49.120,0:07:50.150 So I get twenty-six. 0:07:50.160,0:07:51.940 Three times eight is twenty-four. 0:07:51.940,0:07:54.510 Plus two is twenty-six. 0:07:54.520,0:07:57.760 Two hundred sixty-seven. 0:07:57.760,0:07:59.135 Now I'm going to do another one, 0:07:59.135,0:08:04.147 but I'm going to up the stakes a little bit. 0:08:04.147,0:08:06.689 Just when you thought you were getting comfortable with this, 0:08:06.689,0:08:09.177 I'm going to make you uncomfortable! 0:08:09.177,0:08:20.374 Let's do two hundred thirty-nine times six. 0:08:20.374,0:08:23.178 I thought this was a video about two-digit multiplication times one-digit. 0:08:23.178,0:08:24.712 Well, it is, but I just want to show you 0:08:24.712,0:08:27.992 that you can really do any number of digits times this one digit, 0:08:27.992,0:08:29.562 and it's really the same process. 0:08:29.562,0:08:32.480 You could probably guess how we're going to do it. 0:08:32.480,0:08:34.446 So what's six times nine? 0:08:34.446,0:08:35.870 Let me write it here. 0:08:35.870,0:08:37.870 Six times nine. 0:08:37.880,0:08:39.430 We saw this show before. 0:08:39.440,0:08:41.670 This is fifty-four. 0:08:41.670,0:08:45.080 So we put the four down here, we put the five in the tens place 0:08:45.090,0:08:48.640 because the fifty in fifty-four is really five tens. 0:08:48.640,0:08:49.820 Fair enough. 0:08:49.830,0:08:52.184 Now we're going to do six times three. 0:08:52.184,0:08:54.397 So six times three, 0:08:54.397,0:08:56.742 that's equal to eighteen. 0:08:56.742,0:08:58.530 We still have that five hanging out there, 0:08:58.530,0:09:02.178 so we have to add that five up there and we get-- 0:09:02.178,0:09:03.682 what's eighteen plus five? 0:09:03.682,0:09:10.160 So six times three is eighteen, plus five is twenty-three. 0:09:10.160,0:09:10.902 Just to be clear, 0:09:10.902,0:09:13.788 we didn't multiply six times three and add five. 0:09:13.788,0:09:14.645 We actually, 0:09:14.645,0:09:18.360 if you looked at where we are in our place on the problem, 0:09:18.360,0:09:19.973 this is actually a thirty. 0:09:19.973,0:09:21.400 I just happened to do a three here. 0:09:21.400,0:09:24.490 But this is six times thirty plus fifty. 0:09:24.500,0:09:27.830 Because thirty-nine is three tens or thirty. 0:09:27.830,0:09:32.200 So this number, actually, even though we said six times three is eighteen. 0:09:32.200,0:09:34.140 Plus five is twenty-three. 0:09:34.140,0:09:36.390 This number is really two hundred thirty. 0:09:36.400,0:09:38.790 So we put the three in the tens place. 0:09:38.800,0:09:41.490 Actually, let me do it in a different color 0:09:41.490,0:09:43.800 than what I did up here. 0:09:43.800,0:09:46.380 This is equal to twenty-three. 0:09:46.380,0:09:49.228 We can put the three in the tens place 0:09:49.228,0:09:52.610 and then put this two up here. 0:09:52.610,0:09:57.350 Now we're almost done, one multiplication left. 0:09:57.350,0:10:01.140 This is the six times the two. 0:10:01.140,0:10:02.290 That's an easy one. 0:10:02.300,0:10:03.490 That's twelve. 0:10:03.500,0:10:06.710 But I have this other two hanging out up here, 0:10:06.710,0:10:08.320 so I have to add this other two. 0:10:08.320,0:10:09.770 So plus two. 0:10:09.770,0:10:12.251 And what is that equal to? 0:10:12.251,0:10:15.025 That is equal to 0:10:15.025,0:10:17.365 twelve plus two is equal to fourteen. 0:10:17.370,0:10:18.620 So I write the four. 0:10:18.620,0:10:20.120 So six times two is twelve. 0:10:20.130,0:10:21.830 Plus two is fourteen. 0:10:21.840,0:10:23.500 I write the four down here. 0:10:23.500,0:10:25.497 If there was any more digits I would write the one up there, 0:10:25.497,0:10:26.740 but there aren't any more digits. 0:10:26.740,0:10:29.090 So I write the one over here. 0:10:29.090,0:10:35.210 So two hundred thirty-nine times six is one thousand four hundred thirty-four. 0:10:35.210,0:10:38.197 Let's do another one. 0:10:38.197,0:10:40.980 I need to get some space cleaned out. 0:10:40.980,0:10:42.869 And hey, while we're escalating the situation, 0:10:42.869,0:10:46.615 let's go to four-digits. 0:10:46.615,0:10:53.058 Let's do seven thousand three hundred sixty-two times-- 0:10:53.058,0:10:53.814 let's do a hard one. 0:10:53.814,0:10:56.210 Times nine. 0:10:56.220,0:10:58.320 So what's nine times two? 0:10:58.320,0:10:59.900 And I won't do this side math over here. 0:10:59.900,0:11:01.260 I think you're getting the pattern. 0:11:01.260,0:11:03.380 What's nine times two? 0:11:03.390,0:11:06.202 Nine times two is eighteen. 0:11:06.202,0:11:08.130 Eighteen. 0:11:08.145,0:11:10.125 Then we do nine times six. 0:11:10.130,0:11:13.960 Nine times six is fifty-four. 0:11:13.970,0:11:18.675 And fifty-four plus one is fifty-five. 0:11:18.675,0:11:20.841 Fifty-five. 0:11:20.841,0:11:23.254 What's nine times three? 0:11:23.270,0:11:27.140 Nine times three is twenty-seven-- if we have that memorized. 0:11:27.140,0:11:34.370 And then twenty-seven plus five is thirty-two. 0:11:34.370,0:11:36.348 Let me switch colors. 0:11:36.348,0:11:38.961 Thirty-two. 0:11:38.961,0:11:40.707 And then you have nine times seven. 0:11:40.710,0:11:44.158 That's sixty-three, but we have this three hanging out there. 0:11:44.158,0:11:47.350 So that's nine times seven is sixty-three, 0:11:47.360,0:11:50.460 plus three is sixty-six. 0:11:50.460,0:11:52.032 You write the six here, 0:11:52.032,0:11:54.552 and then you have no where to put the sixty in the sixty-six, 0:11:54.552,0:11:56.872 so you write that down here as well. 0:11:56.872,0:12:00.494 And so seven thousand three hundred sixty-two times nine 0:12:00.494,0:12:05.024 is sixty-six thousand two hundred fifty-eight. 0:12:05.024,0:12:07.200 Hopefully you found that useful.