0:00:00.740,0:00:03.400 Let's now see if we can divide into larger numbers. 0:00:03.400,0:00:06.860 And just as a starting point, in order to divide into larger numbers, 0:00:06.860,0:00:09.920 you at least need to know your multiplication tables 0:00:09.920,0:00:14.550 from the one-multiplication tables all the way to, at least, the ten-multiplication. 0:00:14.550,0:00:17.080 So all the way up to ten times ten, which you know is one hundred. 0:00:17.080,0:00:20.055 And then, starting at one times one and going up to two times three, 0:00:20.055,0:00:22.320 all the way up to ten times ten. 0:00:22.320,0:00:23.842 And, at least when I was in school, 0:00:23.842,0:00:25.340 we learned through twelve times twelve. 0:00:25.340,0:00:28.100 But ten times ten will probably do the trick. 0:00:28.100,0:00:29.770 And that's really just the starting point. 0:00:29.770,0:00:32.550 Because to do multiplication problems like this, 0:00:32.550,0:00:34.150 for example, or division problems like this. 0:00:34.150,0:00:39.640 Let's say I'm taking twenty-five and I want to divide it by five. 0:00:39.640,0:00:41.118 So I could draw twenty-five objects, 0:00:41.118,0:00:44.558 and then divide them into groups of five or divide them into five groups, 0:00:44.558,0:00:47.590 and see how many elements are in each group. 0:00:47.590,0:00:49.562 But the quick way to do is just to think about, 0:00:49.562,0:00:52.930 well, five times what is twenty-five, right? 0:00:52.930,0:00:58.100 Five times question mark is equal to twenty-five. 0:00:58.100,0:00:59.860 And if you know your multiplication tables, 0:00:59.860,0:01:02.070 especially your five-multiplication tables, 0:01:02.070,0:01:06.280 you know that five times five is equal to twenty-five. 0:01:06.280,0:01:08.834 So something like this, you'll immediately just be able to say, 0:01:08.849,0:01:11.692 because of your knowledge of multiplication, 0:01:11.692,0:01:14.840 that five goes into twenty-five five times. 0:01:14.840,0:01:16.243 And you'd write the five right there. 0:01:16.243,0:01:17.180 Not over the two, 0:01:17.180,0:01:20.040 because you still want to be careful of the place notation. 0:01:20.040,0:01:21.650 You want to write the five in the ones place. 0:01:21.650,0:01:25.480 It goes into it five ones times, or exactly five times. 0:01:25.480,0:01:26.190 And the same thing. 0:01:26.190,0:01:31.770 If I said seven goes into forty-nine. 0:01:31.770,0:01:33.250 That's how many times? 0:01:33.250,0:01:36.772 Well you say, that's like saying seven times what-- 0:01:36.772,0:01:39.373 you could even, instead of a question mark, you could put a blank there-- 0:01:39.388,0:01:43.130 seven times what is equal to forty-nine? 0:01:43.130,0:01:45.452 And if you know your multiplication tables, 0:01:45.452,0:01:50.090 you know that seven times seven is equal to forty-nine. 0:01:50.090,0:01:53.145 All the examples I've done so far is a number multiplied by itself. 0:01:53.150,0:01:55.030 Let me do another example. 0:01:55.030,0:02:01.840 Let me do nine goes into fifty-four how many times? 0:02:01.840,0:02:05.102 Once again, you need to know your multiplication tables to do this. 0:02:05.102,0:02:09.290 Nine times what is equal to fifty-four? 0:02:09.290,0:02:10.904 And sometimes, even if you don't have it memorized, 0:02:10.904,0:02:14.720 you could say nine times five is forty-five. 0:02:14.720,0:02:19.470 And nine times six would be nine more than that, so that would be fifty-four. 0:02:19.470,0:02:22.380 So nine goes into fifty-four six times. 0:02:22.380,0:02:23.590 So just as a starting point, 0:02:23.590,0:02:27.253 you need to have your multiplication tables from one times one 0:02:27.253,0:02:29.250 all the way up the ten times ten memorized. 0:02:29.250,0:02:36.689 In order to be able to do at least some of these more basic problems relatively quickly. 0:02:36.700,0:02:38.968 Now, with that out of the way, let's try to do some problems 0:02:38.968,0:02:44.015 that might not fit completely cleanly into your multiplication tables. 0:02:44.015,0:02:46.190 So let's say I want to divide-- 0:02:46.190,0:02:54.800 I am looking to divide three into forty-three. 0:02:54.800,0:02:58.440 And, once again, this is larger than three times ten or three times twelve. 0:02:58.440,0:02:58.930 Actually, look. 0:02:58.930,0:03:00.950 Well, let me do another problem. 0:03:00.950,0:03:04.260 Let me do three into twenty-three. 0:03:04.260,0:03:06.165 And, if you know your three-times tables, 0:03:06.165,0:03:10.060 you realize that there's three times nothing is exactly twenty-three. 0:03:10.060,0:03:10.910 I'll do it right now. 0:03:10.910,0:03:13.280 Three times one is three. 0:03:13.280,0:03:15.690 Three times two is six. 0:03:15.690,0:03:16.870 Let me just write them all out. 0:03:16.870,0:03:24.690 Three times three is nine, twelve, fifteen, eighteen, twenty-one, twenty-four, right? 0:03:24.690,0:03:27.700 There's no twenty-three in the multiples of three. 0:03:27.700,0:03:29.700 So how do you do this division problem? 0:03:29.700,0:03:34.434 Well what you do is you think of what is the largest multiple of three that does go into twenty-three? 0:03:34.440,0:03:36.640 And that's twenty-one. 0:03:36.640,0:03:39.170 And three goes into twenty-one how many times? 0:03:39.170,0:03:44.150 Well you know that three times seven is equal to twenty-one. 0:03:44.150,0:03:48.520 So you say, well three will go into twenty-three seven times. 0:03:48.520,0:03:50.570 But it doesn't go into it cleanly, 0:03:50.570,0:03:53.850 because seven times three is twenty-one. 0:03:53.850,0:03:55.750 So there's a remainder left over. 0:03:55.750,0:04:00.170 So if you take twenty-three minus twenty-one, you have a remainder of two. 0:04:00.170,0:04:08.010 So you could write that twenty-three divided by three is equal to seven, 0:04:08.010,0:04:14.995 remainder-- maybe I'll just, well, write the whole word out --remainder two. 0:04:15.010,0:04:17.050 So it doesn't have to go in completely cleanly. 0:04:17.050,0:04:19.790 And, in the future, we'll learn about decimals and fractions. 0:04:19.790,0:04:22.747 But for now, you just say, well it goes in cleanly seven times, 0:04:22.747,0:04:24.290 but that only gets us to twenty-one. 0:04:24.290,0:04:26.110 But then there's two left over. 0:04:26.110,0:04:28.507 So you can even work with the division problems 0:04:28.507,0:04:31.078 where it's not exactly a multiple of the number 0:04:31.078,0:04:33.310 that you're dividing into the larger number. 0:04:33.310,0:04:37.720 But let's do some practice with even larger numbers. 0:04:37.720,0:04:40.520 And I think you'll see a pattern here. 0:04:40.520,0:04:47.058 So let's do four going into-- 0:04:47.058,0:04:51.800 I'm going to pick a pretty large number here --three hundred forty-four. 0:04:51.800,0:04:53.694 And, immediately when you see that, 0:04:53.694,0:04:57.850 you might say, hey Sal, I know up to four times ten or four times twelve. 0:04:57.850,0:04:59.850 Four times twelve is forty-eight. 0:04:59.850,0:05:01.340 This is a much larger number. 0:05:01.340,0:05:02.767 This is way out of bounds 0:05:02.767,0:05:05.420 of what I know in my four-multiplication tables. 0:05:05.420,0:05:08.379 And what I'm going to show you right now is a way of doing this, 0:05:08.379,0:05:10.910 just knowing your four-multiplication tables. 0:05:10.910,0:05:11.889 So what you do is you say 0:05:11.889,0:05:16.800 four goes into this three how many times? 0:05:16.800,0:05:17.479 And you're actually saying 0:05:17.479,0:05:20.430 four goes into this three how many hundred times? 0:05:20.430,0:05:22.590 So this is-- because this is three hundred, right? 0:05:22.590,0:05:24.880 This is three hundred forty-four. 0:05:24.880,0:05:29.934 But four goes into three no hundred times, or four goes into-- 0:05:29.949,0:05:32.810 I guess the best way to think of it --four goes three zero times. 0:05:32.810,0:05:34.470 So you can just move on. 0:05:34.470,0:05:36.260 Four goes into thirty-four. 0:05:36.260,0:05:41.460 So now we're going to focus on the thirty-four. 0:05:41.460,0:05:43.900 So four goes into thirty-four how many times? 0:05:43.900,0:05:46.900 And here we can use our four-multiplication tables. 0:05:46.900,0:05:51.950 Four-- Let's see, four times eight is equal to thirty-two. 0:05:51.950,0:05:56.210 Four times nine is equal to thirty-six. 0:05:56.210,0:05:59.630 So four goes into thirty-four-- nine is too many times, right? 0:05:59.630,0:06:01.500 Thirty-six is larger than thirty-four. 0:06:01.500,0:06:03.746 So four goes into thirty-four eight times. 0:06:03.746,0:06:06.089 There's going to be a little bit left over. 0:06:06.089,0:06:09.032 Four goes into thirty-four eight times. 0:06:09.032,0:06:10.856 So let's figure out what's left over. 0:06:10.856,0:06:11.565 And really we're saying, 0:06:11.565,0:06:14.947 four goes into three hundred forty how many ten times? 0:06:14.947,0:06:17.807 So we're actually saying four goes into three hundred forty eighty times. 0:06:17.807,0:06:20.020 Because notice we wrote this eight in the tens place. 0:06:20.020,0:06:22.882 But just for our ability to do this problem quickly, 0:06:22.882,0:06:24.954 you just say four goes into thirty-four eight times, 0:06:24.954,0:06:28.770 but make sure you write the eight in the tens place right there. 0:06:28.770,0:06:30.100 Eight times four. 0:06:30.100,0:06:30.970 We already know what that is. 0:06:30.970,0:06:34.140 Eight times four is thirty-two. 0:06:34.140,0:06:36.290 And then we figure out the remainder. 0:06:36.290,0:06:38.160 Thirty-four minus thirty-two. 0:06:38.160,0:06:40.400 Well, four minus two is two. 0:06:40.400,0:06:42.030 And then these threes cancel out. 0:06:42.030,0:06:43.300 So you're just left with a two. 0:06:43.300,0:06:46.120 But notice we're in the tens column, right? 0:06:46.120,0:06:48.710 This whole column right here, that's the tens column. 0:06:48.710,0:06:55.120 So really what we said is four goes into three hundred forty eighty times. 0:06:55.120,0:06:58.350 Eighty times four is three hundred twenty, right? 0:06:58.350,0:07:00.844 Because I wrote the three in the hundreds column. 0:07:00.844,0:07:05.701 And then, there is-- 0:07:05.701,0:07:07.215 let me clean this up a little bit. 0:07:07.215,0:07:08.872 I didn't want to make that line there look like a-- 0:07:08.872,0:07:10.510 when I was dividing the columns-- to look like a one. 0:07:10.510,0:07:11.934 But then there's a remainder of two, 0:07:11.934,0:07:14.270 but I wrote the two in the tens place. 0:07:14.270,0:07:15.740 So it's actually a remainder of twenty. 0:07:15.740,0:07:16.990 But let me bring down this four. 0:07:16.990,0:07:18.660 Because I didn't want to just divide into three hundred forty. 0:07:18.660,0:07:20.290 I divided into three hundred forty-four. 0:07:20.290,0:07:22.290 So you bring down the four. 0:07:22.290,0:07:24.440 Let me switch colors. 0:07:24.440,0:07:26.670 And then-- So another way to think about it. 0:07:26.670,0:07:31.250 We just said that four goes into three hundred forty-four eighty times, right? 0:07:31.250,0:07:33.050 We wrote the eight in the tens place. 0:07:33.050,0:07:35.550 And then eight times four is three hundred twenty. 0:07:35.550,0:07:38.170 The remainder is now twenty-four. 0:07:38.170,0:07:40.800 So how many times does four go into twenty-four? 0:07:40.800,0:07:41.631 Well we know that. 0:07:41.631,0:07:46.158 Four times six is equal to twenty-four. 0:07:46.158,0:07:49.107 So four goes into twenty-four six times. 0:07:49.107,0:07:50.685 And we put that in the ones place. 0:07:50.685,0:07:53.480 Six times four is twenty-four. 0:07:53.480,0:07:54.560 And then we subtract. 0:07:54.560,0:07:56.270 Twenty-four minus twenty-four. 0:07:56.270,0:07:58.490 That's-- We subtract at that stage, either case. 0:07:58.490,0:07:59.530 And we get zero. 0:07:59.530,0:08:01.050 So there's no remainder. 0:08:01.050,0:08:05.850 So four goes into three hundred forty-four exactly eighty-six times. 0:08:05.850,0:08:09.180 So if your took three hundred forty-four objects and divided them into groups of four, 0:08:09.180,0:08:10.900 you would get eighty-six groups. 0:08:10.900,0:08:12.950 Or if you divided them into groups of eighty-six, 0:08:12.950,0:08:13.880 you would get four groups. 0:08:13.880,0:08:15.640 Let's do a couple more problems. 0:08:15.640,0:08:18.440 I think you're getting the hang of it. 0:08:18.440,0:08:21.180 Let me do seven-- I'll do a simple one. 0:08:21.180,0:08:24.790 Seven goes into ninety-one. 0:08:24.790,0:08:28.387 So once again, well, this is beyond seven times twelve, 0:08:28.387,0:08:31.340 which is eighty-four, which you know from our multiplication tables. 0:08:31.340,0:08:34.650 So we use the same system we did in the last problem. 0:08:34.650,0:08:37.750 Seven goes into nine how many times? 0:08:37.750,0:08:41.220 Seven goes into nine one time. 0:08:41.220,0:08:44.640 One times seven is seven. 0:08:44.640,0:08:48.330 And you have nine minus seven is two. 0:08:48.330,0:08:51.190 And then you bring down the one. 0:08:51.190,0:08:51.770 Twenty-one. 0:08:51.770,0:08:53.036 And remember, this might seem like magic, 0:08:53.036,0:08:57.545 but what we really said was seven goes into ninety ten[br]times-- 0:08:57.545,0:08:59.961 ten because we wrote the one in the tens place-- 0:08:59.961,0:09:02.466 ten times seven is seventy. 0:09:02.466,0:09:05.053 Right?-- You could almost put a zero there if you like-- 0:09:05.053,0:09:08.380 And ninety-one minus seventy is twenty-one. 0:09:08.380,0:09:12.640 So seven goes into ninety-one ten times remainder twenty-one. 0:09:12.640,0:09:15.780 And then you say seven goes into twenty-one-- Well you know that. 0:09:15.780,0:09:17.590 Seven times three is twenty-one. 0:09:17.590,0:09:20.170 So seven goes into twenty-one three times. 0:09:20.170,0:09:22.710 Three times seven is twenty-one. 0:09:22.710,0:09:24.550 You subtract these from each other. 0:09:24.550,0:09:26.375 Remainder zero. 0:09:26.375,0:09:31.908 So ninety-one divided by seven is equal to thirteen. 0:09:31.908,0:09:32.530 Let's do another one. 0:09:32.530,0:09:35.863 And I won't take that little break to explain the places and all of that. 0:09:35.863,0:09:36.800 I think you understand that. 0:09:36.800,0:09:41.569 I want, at least, you to get the process down really really well in this video. 0:09:41.580,0:09:44.990 So let's do seven-- I keep using the number seven. 0:09:44.990,0:09:46.510 Let me do a different number. 0:09:46.510,0:09:56.560 Let me do eight goes into six hundred eight how many times? 0:09:56.560,0:09:59.440 So I go eight goes into six how many times? 0:09:59.440,0:10:00.740 It goes into it zero times. 0:10:00.740,0:10:01.980 So let me keep moving. 0:10:01.980,0:10:05.360 Eight goes into sixty how many times? 0:10:05.360,0:10:06.820 Let me write down the eight. 0:10:06.820,0:10:09.110 Let me draw a line here so we don't get confused. 0:10:09.110,0:10:11.340 Let me scroll down a little bit. 0:10:11.340,0:10:13.760 I need some space above the number. 0:10:13.760,0:10:15.580 So eight goes into sixty how many times? 0:10:15.580,0:10:19.590 We know that eight times seven is equal to fifty-six. 0:10:19.590,0:10:23.330 And that eight times eight is equal to sixty-four. 0:10:23.330,0:10:25.640 So eight goes into-- sixty-four is too big. 0:10:25.640,0:10:26.770 So it's not this one. 0:10:26.771,0:10:29.876 So eight goes into sixty, seven times. 0:10:29.876,0:10:31.740 There's going to be a little bit left over. 0:10:31.740,0:10:34.600 So eight goes into sixty, seven times. 0:10:34.600,0:10:35.728 Since we're doing the whole sixty, 0:10:35.728,0:10:38.799 we put the seven above the ones place in the sixty, 0:10:38.799,0:10:41.062 which is the tens place in the whole thing. 0:10:41.062,0:10:44.970 Seven times eight, we know, is fifty-six. 0:10:44.970,0:10:47.100 Sixty minus fifty-six. 0:10:47.100,0:10:48.030 That's four. 0:10:48.030,0:10:48.990 We could do that in our heads. 0:10:48.990,0:10:50.270 Or if we wanted, we can borrow. 0:10:50.270,0:10:51.510 That be a ten. 0:10:51.510,0:10:53.380 That would be a five. 0:10:53.380,0:10:54.890 Ten minus six is four. 0:10:54.890,0:10:59.930 Then you bring down this eight. 0:10:59.930,0:11:02.738 Eight goes into forty-eight how many times? 0:11:02.750,0:11:06.260 Well what's eight times six? 0:11:06.260,0:11:09.210 Well, eight times six is exactly forty-eight. 0:11:09.210,0:11:13.170 So eight times-- eight goes into forty-eight six times. 0:11:13.170,0:11:17.180 Six times eight is forty-eight. 0:11:17.180,0:11:18.180 And you subtract. 0:11:18.180,0:11:19.500 We subtracted up here as well. 0:11:19.500,0:11:22.020 Forty-eight minus forty-eight is zero. 0:11:22.020,0:11:25.260 So, once again, we get a remainder of zero. 0:11:25.260,0:11:28.798 So hopefully, that gives you the hang of how to do these larger division problems. 0:11:28.798,0:11:31.012 And all we really need to know to be able to do these, 0:11:31.012,0:11:34.242 to tackle these, is our multiplication tables 0:11:34.242,0:11:38.381 up to maybe ten times ten or twelve times twelve.