1 00:00:00,730 --> 00:00:04,267 I think you've probably heard the word divide before, 2 00:00:04,267 --> 00:00:06,730 where someone tells you to divide something up. 3 00:00:06,730 --> 00:00:10,450 Divide the money between you and your brother 4 00:00:10,450 --> 00:00:12,650 or between you and your buddy. 5 00:00:12,650 --> 00:00:14,640 And it essentially means to cut up something. 6 00:00:14,640 --> 00:00:20,458 So let me write down the word divide. 7 00:00:20,458 --> 00:00:24,328 Let's say that I have four quarters. 8 00:00:24,328 --> 00:00:27,500 Do my best to draw the quarters. 9 00:00:27,500 --> 00:00:32,320 If I have four quarters just like that. 10 00:00:32,320 --> 00:00:36,030 That's my rendition of George Washington on the quarters. 11 00:00:36,030 --> 00:00:37,620 And let's say there's two of us, 12 00:00:37,620 --> 00:00:40,550 and we're going to divide the quarters between us. 13 00:00:40,550 --> 00:00:42,520 So this is me right here. 14 00:00:42,520 --> 00:00:45,870 Let me try my best to draw me. 15 00:00:45,870 --> 00:00:48,760 So that's me right there. 16 00:00:48,760 --> 00:00:51,160 Let's see, I have a lot of hair. 17 00:00:51,160 --> 00:00:55,705 And then this is you right there. 18 00:00:55,705 --> 00:00:57,300 I'll do my best. 19 00:00:57,300 --> 00:00:59,270 Let's say you're bald. 20 00:00:59,270 --> 00:01:04,407 But you have side burns. 21 00:01:04,407 --> 00:01:09,077 Maybe you have a little bit of a beard. 22 00:01:09,090 --> 00:01:10,317 So that's you, that's me, 23 00:01:10,317 --> 00:01:15,520 and we're going to divide these four quarters between the two of us. 24 00:01:15,520 --> 00:01:20,876 So notice, we have four quarters 25 00:01:20,876 --> 00:01:23,580 and we're going to divide between the two of us. 26 00:01:23,580 --> 00:01:26,540 There are two of us. 27 00:01:26,540 --> 00:01:28,740 And I want to stress the number two. 28 00:01:28,740 --> 00:01:31,880 So we're going to divide four quarters by two. 29 00:01:31,880 --> 00:01:34,480 We're going to divide it between the two of us. 30 00:01:34,480 --> 00:01:36,900 And you've probably done something like this. 31 00:01:36,900 --> 00:01:37,540 What happens? 32 00:01:37,540 --> 00:01:40,230 Well, each of us are going to get two quarters. 33 00:01:40,230 --> 00:01:41,290 So let me divide it. 34 00:01:41,290 --> 00:01:43,180 We're going to divide it into two. 35 00:01:43,180 --> 00:01:46,060 Essentially what I did do is I take the four quarters 36 00:01:46,075 --> 00:01:48,954 and I divide it into two equal groups. 37 00:01:48,954 --> 00:01:51,697 Two equal groups. 38 00:01:51,712 --> 00:01:53,931 And that's what division is. 39 00:01:53,931 --> 00:01:57,620 We cut up this group of quarters into two equal groups. 40 00:01:57,620 --> 00:02:01,012 So when you divide four quarters into two groups, 41 00:02:01,012 --> 00:02:08,061 so this was four quarters right there. 42 00:02:08,061 --> 00:02:09,592 And you want to divide it into two groups. 43 00:02:09,592 --> 00:02:11,770 This is group one. 44 00:02:11,770 --> 00:02:16,530 Group one right here. 45 00:02:16,530 --> 00:02:19,380 And this is group two right here. 46 00:02:19,380 --> 00:02:21,890 How many numbers are in each group? 47 00:02:21,890 --> 00:02:23,990 Or how many quarters are in each group? 48 00:02:23,990 --> 00:02:26,870 Well, in each group I have one, two quarters. 49 00:02:26,870 --> 00:02:28,660 I'll need to use a brighter color. 50 00:02:28,660 --> 00:02:31,260 I have one, two quarters in each group. 51 00:02:31,260 --> 00:02:34,040 One quarter and two quarters in each group. 52 00:02:34,040 --> 00:02:36,153 So to write this out mathematically, 53 00:02:36,153 --> 00:02:37,855 I think this is something that you've done, 54 00:02:37,855 --> 00:02:40,728 probably as long as you've been splitting money 55 00:02:40,728 --> 00:02:42,882 between you and your siblings and your buddies. 56 00:02:42,882 --> 00:02:44,066 Actually, let me scroll over a little bit, 57 00:02:44,066 --> 00:02:47,330 so you can see my entire picture. 58 00:02:47,330 --> 00:02:50,360 How do we write this mathematically? 59 00:02:50,360 --> 00:02:55,270 We can write that four divided by-- so this four. 60 00:02:55,270 --> 00:02:56,980 Let me use the right colors. 61 00:02:56,980 --> 00:03:03,758 So this four, which is this four, divided by the two groups, 62 00:03:03,758 --> 00:03:07,500 these are the two groups: group one and this is group two right here. 63 00:03:07,500 --> 00:03:11,030 So divided into two groups or into two collections. 64 00:03:11,030 --> 00:03:14,953 Four divided by two is equal to-- 65 00:03:14,953 --> 00:03:17,850 when you divide four into two groups, 66 00:03:17,850 --> 00:03:20,361 each group is going to have two quarters in it. 67 00:03:20,361 --> 00:03:22,918 It's going to be equal to two. 68 00:03:22,918 --> 00:03:24,388 And I just wanted to use this example 69 00:03:24,388 --> 00:03:25,149 because I want to show you 70 00:03:25,149 --> 00:03:29,260 that division is something that you've been using all along. 71 00:03:29,260 --> 00:03:32,822 And another important, I guess, takeaway or thing to realize about this, 72 00:03:32,822 --> 00:03:36,328 is on some level this is the opposite of multiplication. 73 00:03:36,330 --> 00:03:42,564 If I said that I had two groups of two quarters, 74 00:03:42,564 --> 00:03:48,694 I would multiply the two groups times the two quarters each 75 00:03:48,694 --> 00:03:52,849 and I would say I would then have four quarters. 76 00:03:52,849 --> 00:03:55,886 So on some level, these are saying the same thing. 77 00:03:55,901 --> 00:03:58,538 But just to make it a little bit more concrete in our head, 78 00:03:58,538 --> 00:04:01,400 let's do a couple of more examples. 79 00:04:01,400 --> 00:04:03,600 Let's do a bunch of more examples. 80 00:04:03,600 --> 00:04:08,681 So let's write down, what is six divided by-- 81 00:04:08,681 --> 00:04:10,900 I'm trying to keep it nice and color coded. 82 00:04:10,900 --> 00:04:14,800 Six divided by three, what is that equal to? 83 00:04:14,800 --> 00:04:17,150 Let's just draw six objects. 84 00:04:17,150 --> 00:04:18,590 They can be anything. 85 00:04:18,590 --> 00:04:23,030 Let's say I have six bell peppers. 86 00:04:23,030 --> 00:04:25,050 I won't take too much trouble to draw them. 87 00:04:25,050 --> 00:04:27,260 Well, that's not what a bell pepper looks like, 88 00:04:27,260 --> 00:04:28,210 but you get the idea. 89 00:04:28,210 --> 00:04:34,370 So one, two, three, four, five, six. 90 00:04:34,370 --> 00:04:36,030 And I'm going to divide it by three. 91 00:04:36,030 --> 00:04:37,700 And one way that we can think about that 92 00:04:37,700 --> 00:04:41,059 is that means I want to divide my six bell peppers 93 00:04:41,059 --> 00:04:43,730 into three equal groups of bell peppers. 94 00:04:43,730 --> 00:04:47,384 You could kind of think of it as if three people are going to share these bell peppers, 95 00:04:47,384 --> 00:04:48,970 how many do each of them get? 96 00:04:48,970 --> 00:04:50,840 So let's divide it into three groups. 97 00:04:50,840 --> 00:04:52,770 So that's our six bell peppers. 98 00:04:52,770 --> 00:04:54,580 I'm going to divide it into three groups. 99 00:04:54,580 --> 00:04:56,564 So the best way to divide it into three groups is 100 00:04:56,564 --> 00:05:02,470 I can have one group right there, two groups, or the second group right there, 101 00:05:02,470 --> 00:05:04,910 and then, the third group. 102 00:05:04,910 --> 00:05:10,350 And then each group will have exactly how many bell peppers? 103 00:05:10,350 --> 00:05:12,120 They'll have one, two. 104 00:05:12,120 --> 00:05:13,510 One, two. 105 00:05:13,510 --> 00:05:15,140 One, two bell peppers. 106 00:05:15,140 --> 00:05:20,060 So six divided by three is equal to two. 107 00:05:20,060 --> 00:05:22,384 So the best way or one way to think about it 108 00:05:22,384 --> 00:05:26,790 is that you divided the six into three groups. 109 00:05:26,790 --> 00:05:29,880 Now you could view that a slightly different way, 110 00:05:29,880 --> 00:05:31,392 although it's not completely different, 111 00:05:31,392 --> 00:05:33,110 but it's a good way to think about it. 112 00:05:33,110 --> 00:05:38,150 You could also think of it as six divided by three. 113 00:05:38,150 --> 00:05:42,936 And once again, let's say I have raspberries now-- easier to draw. 114 00:05:42,952 --> 00:05:47,460 One, two, three, four, five, six. 115 00:05:47,460 --> 00:05:51,598 And here, instead of dividing it into three groups like we did here. 116 00:05:51,600 --> 00:05:54,290 This was one group, two group, three groups. 117 00:05:54,290 --> 00:05:56,165 Instead of dividing into three groups, 118 00:05:56,165 --> 00:05:57,521 what I want to do is say well, 119 00:05:57,521 --> 00:06:02,710 if I'm dividing six divided by three, I want to divide it into groups of three. 120 00:06:02,710 --> 00:06:04,260 Not into three groups. 121 00:06:04,260 --> 00:06:05,960 I want to divide it into groups of three. 122 00:06:05,960 --> 00:06:09,490 So how many groups of three am I going to have? 123 00:06:09,490 --> 00:06:12,930 Well, let me draw some groups of three. 124 00:06:12,930 --> 00:06:16,040 So that is one group of three. 125 00:06:16,040 --> 00:06:21,725 And that is two groups of three. 126 00:06:21,725 --> 00:06:26,674 So if I take six things and I divide them into groups of three, 127 00:06:26,674 --> 00:06:29,950 I will end up with one, two groups. 128 00:06:29,950 --> 00:06:33,230 So that's another way to think about division. 129 00:06:33,230 --> 00:06:34,550 And this is an interesting thing. 130 00:06:34,550 --> 00:06:36,908 When you think about these two relations, 131 00:06:36,908 --> 00:06:42,120 you'll see a relationship between six divided by three and six divided by two. 132 00:06:42,120 --> 00:06:43,720 Let me do that right here. 133 00:06:43,720 --> 00:06:48,483 What is six divided by two, 134 00:06:48,483 --> 00:06:51,740 when you think of it in this context right here? 135 00:06:51,740 --> 00:06:54,850 Six divided by two, when you do it like that-- 136 00:06:54,850 --> 00:06:58,780 let me draw one, two, three, four, five, six. 137 00:06:58,780 --> 00:07:03,286 When we think about six divided by two in terms of dividing it into two groups, 138 00:07:03,286 --> 00:07:06,725 what we can end up is we could have one group like this 139 00:07:06,725 --> 00:07:08,674 and then one group like this, 140 00:07:08,674 --> 00:07:11,500 and each group will have three elements. 141 00:07:11,500 --> 00:07:12,541 It'll have three things in it. 142 00:07:12,541 --> 00:07:14,730 So six divided by two is three. 143 00:07:14,730 --> 00:07:16,400 Or you could think of it the other way. 144 00:07:16,400 --> 00:07:21,683 You could say that six divided by two is-- 145 00:07:21,683 --> 00:07:26,420 you're taking six objects: one, two, three, four, five, six. 146 00:07:26,420 --> 00:07:29,041 And your dividing it into groups of two 147 00:07:29,041 --> 00:07:31,200 where each group has two elements. 148 00:07:31,200 --> 00:07:32,920 And that on some level is an easier thing to do. 149 00:07:32,920 --> 00:07:36,640 If each group has two elements, well, that's the one right there. 150 00:07:36,640 --> 00:07:38,690 They don't even have to be nicely ordered. 151 00:07:38,690 --> 00:07:40,900 This could be one group right there 152 00:07:40,900 --> 00:07:42,990 and that could be the other group right there. 153 00:07:42,990 --> 00:07:44,580 I don't have to draw them all stacked up. 154 00:07:44,580 --> 00:07:45,920 These are just groups of two. 155 00:07:45,920 --> 00:07:47,390 But how many groups do I have? 156 00:07:47,390 --> 00:07:49,250 I have one, two, three. 157 00:07:49,250 --> 00:07:51,070 I have three groups. 158 00:07:51,070 --> 00:07:57,706 But notice something, it's no coincidence that six divided by three is two, 159 00:07:57,706 --> 00:08:00,690 and six divided by two is three. 160 00:08:00,690 --> 00:08:03,280 Let me write that down. 161 00:08:03,280 --> 00:08:08,721 We get six divided by three is equal to two, 162 00:08:08,721 --> 00:08:13,290 and six divided by two is equal to three. 163 00:08:13,290 --> 00:08:19,508 And the reason why you see this relation where you can kind of swap this two and this three 164 00:08:19,508 --> 00:08:26,115 is because two times three is equal to six. 165 00:08:26,115 --> 00:08:28,477 Let's say I have two groups of three. 166 00:08:28,490 --> 00:08:29,840 Let me draw two groups of three. 167 00:08:29,840 --> 00:08:37,292 So that's one group of three and then here's another group of three. 168 00:08:37,292 --> 00:08:40,792 So two groups of three is equal to six. 169 00:08:40,792 --> 00:08:44,360 Two times three is equal to six. 170 00:08:44,360 --> 00:08:46,401 Or you could think of it the other way, 171 00:08:46,401 --> 00:08:48,090 if I have three groups of two. 172 00:08:48,090 --> 00:08:50,900 So that's one group of two right there. 173 00:08:50,900 --> 00:08:53,840 I have another group of two right there. 174 00:08:53,840 --> 00:08:56,450 And then I have a third group of two right there. 175 00:08:56,450 --> 00:08:57,960 What is that equal to? 176 00:08:57,960 --> 00:09:01,240 Three groups of two-- three times two. 177 00:09:01,240 --> 00:09:03,260 That's also equal to six. 178 00:09:03,260 --> 00:09:04,840 So two times three is equal to six. 179 00:09:04,840 --> 00:09:05,968 Three times two is equal to six. 180 00:09:05,968 --> 00:09:07,522 We saw this in the multiplication video 181 00:09:07,522 --> 00:09:09,530 that the order doesn't matter. 182 00:09:09,530 --> 00:09:12,182 But that's the reason why if you want to divide it, 183 00:09:12,182 --> 00:09:13,368 if you want to go the other way-- 184 00:09:13,368 --> 00:09:18,990 if you have six things and you want to divide it into groups of two, you get three. 185 00:09:18,990 --> 00:09:23,058 If you have six and you want to divide into groups of three, you get two. 186 00:09:23,070 --> 00:09:24,360 Let's do a couple more problems. 187 00:09:24,360 --> 00:09:33,963 I think it'll really make sense about what division is all about. 188 00:09:33,963 --> 00:09:35,863 Let's do an interesting one. 189 00:09:35,870 --> 00:09:40,600 Let's do nine divided by four. 190 00:09:40,600 --> 00:09:43,360 So if we think about nine divided by four, let me draw nine objects. 191 00:09:43,360 --> 00:09:51,170 One, two, three, four, five, six, seven, eight, nine. 192 00:09:51,170 --> 00:09:54,108 Now when you divide by four, for this problem, 193 00:09:54,108 --> 00:09:57,140 I'm thinking about dividing it into groups of four. 194 00:09:57,140 --> 00:09:58,923 So if I want to divide it into groups of four-- 195 00:09:58,923 --> 00:09:59,899 Let me try doing that. 196 00:09:59,899 --> 00:10:02,521 So here is one group of four. 197 00:10:02,521 --> 00:10:04,820 I just picked any of them right like that. 198 00:10:04,820 --> 00:10:06,570 That's one group of four. 199 00:10:06,570 --> 00:10:11,100 Then here's another group of four, right there. 200 00:10:11,100 --> 00:10:13,330 And then I have this left over thing. 201 00:10:13,330 --> 00:10:15,051 Maybe we could call it a remainder, 202 00:10:15,051 --> 00:10:18,235 where I can't put this one into a group of four. 203 00:10:18,235 --> 00:10:20,793 When I'm dividing by four, 204 00:10:20,793 --> 00:10:24,090 I can only cut up the nine into groups of four. 205 00:10:24,090 --> 00:10:28,102 So the answer here, and this is a new concept for you maybe, 206 00:10:28,102 --> 00:10:32,395 nine divided by four is going to be two groups. 207 00:10:32,395 --> 00:10:34,802 I have one group here, and another group here, 208 00:10:34,802 --> 00:10:36,670 and then I have a remainder of one. 209 00:10:36,670 --> 00:10:38,970 I have one left over that I wasn't able to do with. 210 00:10:38,970 --> 00:10:45,870 Remainder-- that says remainder one. 211 00:10:45,890 --> 00:10:49,348 Nine divided by four is two remainder one. 212 00:10:49,348 --> 00:10:53,010 If I asked you what twelve divided by four is-- so let me do twelve. 213 00:10:53,010 --> 00:11:00,802 One, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve. 214 00:11:00,802 --> 00:11:01,980 So let me write that down. 215 00:11:01,980 --> 00:11:05,918 Twelve divided by four. 216 00:11:05,918 --> 00:11:08,414 So I want to divide these twelve objects-- 217 00:11:08,414 --> 00:11:10,480 maybe they're apples or plums. 218 00:11:10,480 --> 00:11:12,905 And divide them into groups of four. 219 00:11:12,905 --> 00:11:14,845 So let me see if I can do that. 220 00:11:14,845 --> 00:11:19,340 So this is one group of four just like that. 221 00:11:19,340 --> 00:11:23,340 This is another group of four just like that. 222 00:11:23,340 --> 00:11:24,188 And this is pretty straightforward. 223 00:11:24,188 --> 00:11:26,666 And then I have a third group of four. 224 00:11:26,666 --> 00:11:27,996 Just like that. 225 00:11:27,996 --> 00:11:30,750 And there's nothing left over, like I had before. 226 00:11:30,750 --> 00:11:35,210 I can exactly divide twelve objects into three groups of four. 227 00:11:35,210 --> 00:11:38,190 One, two, three groups of four. 228 00:11:38,190 --> 00:11:44,474 So twelve divided by four is equal to three. 229 00:11:44,474 --> 00:11:47,110 And we can do the exercise that we saw on the previous video. 230 00:11:47,110 --> 00:11:49,666 What is twelve divided by three? 231 00:11:49,666 --> 00:11:51,840 Let me do a new color. 232 00:11:51,840 --> 00:11:55,200 Twelve divided by three. 233 00:11:55,200 --> 00:11:56,501 Now based on what we've learn so far, 234 00:11:56,501 --> 00:12:00,884 we say, that should just be four, because three times four is twelve. 235 00:12:00,884 --> 00:12:02,770 But let's prove it to ourselves. 236 00:12:02,770 --> 00:12:09,420 So one, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve. 237 00:12:09,420 --> 00:12:12,180 Let's divide it into groups of three. 238 00:12:12,180 --> 00:12:13,892 And I'm going to make them a little strange looking 239 00:12:13,892 --> 00:12:17,730 just so you see that you don't always have to do it into nice, clean columns. 240 00:12:17,730 --> 00:12:19,870 So that's a group of three, right there. 241 00:12:19,870 --> 00:12:21,680 Twelve divided by three. 242 00:12:21,680 --> 00:12:27,720 Let's see, here is another group of three just like that. 243 00:12:27,720 --> 00:12:33,010 And then, maybe I'll take this group of three like that. 244 00:12:33,010 --> 00:12:34,330 And I'll take this group of three. 245 00:12:34,330 --> 00:12:37,058 There was obviously a much easier way of dividing it up 246 00:12:37,058 --> 00:12:38,684 than doing these weird l-shaped things, 247 00:12:38,684 --> 00:12:40,110 but I want to show you it doesn't matter. 248 00:12:40,110 --> 00:12:42,100 You're just dividing it into groups of three. 249 00:12:42,100 --> 00:12:43,780 And how many groups do we have? 250 00:12:43,780 --> 00:12:45,550 We have one group. 251 00:12:45,550 --> 00:12:49,843 Then we have our second group right here. 252 00:12:49,843 --> 00:12:53,450 And then we have our third group right there. 253 00:12:53,450 --> 00:12:56,610 And then we have-- let me do it in a new color. 254 00:12:56,610 --> 00:12:59,110 And then we have our fourth group right there. 255 00:12:59,110 --> 00:13:01,900 So we have exactly four groups. 256 00:13:01,900 --> 00:13:03,689 And when I say there was an easier way to divide it, 257 00:13:03,689 --> 00:13:08,380 the easier way was obviously-- maybe not obviously-- 258 00:13:08,380 --> 00:13:10,688 if I want to divide these into groups of three, 259 00:13:10,688 --> 00:13:16,740 I could have just done one, two, three, four groups of three. 260 00:13:16,740 --> 00:13:20,706 Either of these, I'm dividing the twelve objects into packets of three. 261 00:13:20,710 --> 00:13:21,790 You can imagine them that way. 262 00:13:21,790 --> 00:13:26,110 Let's do another one that maybe has a remainder. 263 00:13:26,110 --> 00:13:26,967 Let's see. 264 00:13:26,983 --> 00:13:36,348 What is fourteen divided by five? 265 00:13:36,350 --> 00:13:39,580 So let's draw fourteen objects. 266 00:13:39,580 --> 00:13:47,390 One, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve, thirteen, fourteen. 267 00:13:47,390 --> 00:13:48,330 Fourteen objects. 268 00:13:48,330 --> 00:13:51,850 And I'm going to divide it into groups of five. 269 00:13:51,850 --> 00:13:55,510 Well, the easiest thing is there's one group right there, 270 00:13:55,510 --> 00:13:57,930 two groups right there. 271 00:13:57,930 --> 00:13:59,924 But then this last one, I only have four left, 272 00:13:59,924 --> 00:14:01,990 so I can't make another group of five. 273 00:14:01,990 --> 00:14:05,434 So the answer here is I can make two groups of five, 274 00:14:05,434 --> 00:14:10,070 and I'm going to have a remainder-- r for remainder-- of four. 275 00:14:10,070 --> 00:14:11,680 Two remainder four. 276 00:14:11,680 --> 00:14:14,505 Now, once you get enough practice, 277 00:14:14,505 --> 00:14:16,872 you're not always going to be wanting to draw these circles 278 00:14:16,872 --> 00:14:18,270 and dividing them up like that. 279 00:14:18,270 --> 00:14:20,660 Although that would not be incorrect. 280 00:14:20,660 --> 00:14:23,405 So another way to think about this type of problem 281 00:14:23,405 --> 00:14:27,618 is to say, well, fourteen divided by five, how do I figure that out? 282 00:14:27,618 --> 00:14:28,704 Actually, another way of writing this, 283 00:14:28,704 --> 00:14:31,125 and no harm in showing you : 284 00:14:31,125 --> 00:14:36,027 I could say fourteen divided by five is the same thing as fourteen divided by-- 285 00:14:36,027 --> 00:14:38,502 this sign right here-- divided by five. 286 00:14:38,502 --> 00:14:40,060 And what you do is you say, well, let's see. 287 00:14:40,060 --> 00:14:42,750 How many times does five go into fourteen? 288 00:14:42,750 --> 00:14:43,360 Well, let's see. 289 00:14:43,360 --> 00:14:45,971 Five times-- and you kind of do multiplication tables in your head-- 290 00:14:45,971 --> 00:14:48,950 Five times one is equal to five. 291 00:14:48,950 --> 00:14:51,860 Five times two is equal to ten. 292 00:14:51,860 --> 00:14:55,960 So that's still less than fourteen, so five goes at least two times. 293 00:14:55,960 --> 00:14:59,140 Five times three is equal to fifteen. 294 00:14:59,140 --> 00:15:01,650 Well that's bigger than fourteen, so I have to go back here. 295 00:15:01,650 --> 00:15:03,980 So five only goes two times. 296 00:15:03,980 --> 00:15:05,630 So it goes two times. 297 00:15:05,630 --> 00:15:08,530 Two times five is ten. 298 00:15:08,530 --> 00:15:09,690 And then you subtract. 299 00:15:09,690 --> 00:15:12,160 You say fourteen minus ten is four. 300 00:15:12,160 --> 00:15:15,090 And that's the same remainder as right here. 301 00:15:15,090 --> 00:15:17,919 Well, I could divide five into fourteen exactly two times, 302 00:15:17,919 --> 00:15:19,578 which would get us two groups of five. 303 00:15:19,578 --> 00:15:21,090 Which is essentially just ten. 304 00:15:21,090 --> 00:15:28,089 And we still have the four left over. 305 00:15:28,089 --> 00:15:28,858 Let me do a couple of more, 306 00:15:28,858 --> 00:15:35,765 just to really make sure you get this stuff really, really, really, really well. 307 00:15:35,765 --> 00:15:37,542 Let me write it in that notation. 308 00:15:37,542 --> 00:15:41,660 Let's say I do eight divided by two. 309 00:15:41,660 --> 00:15:43,605 And I could also write this as eight-- 310 00:15:43,605 --> 00:15:45,529 so I want to know what that is. 311 00:15:45,529 --> 00:15:46,790 That's a question mark. 312 00:15:46,790 --> 00:15:52,100 I could also write this as eight divided by two. 313 00:15:52,100 --> 00:15:55,019 And the way I do either of these-- I'll draw the circles in a second-- 314 00:15:55,019 --> 00:15:57,655 but the way I do it without drawing the circles, 315 00:15:57,655 --> 00:16:01,219 I say, well, two times one is equal to two. 316 00:16:01,219 --> 00:16:02,683 So that definitely goes into eight, 317 00:16:02,683 --> 00:16:06,062 but maybe I can think of a larger number that goes into-- 318 00:16:06,062 --> 00:16:09,070 that when I multiply it by two still goes into eight. 319 00:16:09,070 --> 00:16:11,360 Two times two is equal to four. 320 00:16:11,360 --> 00:16:13,070 That's still less than eight. 321 00:16:13,070 --> 00:16:15,710 So two times three is equal to six. 322 00:16:15,710 --> 00:16:17,230 Still less than eight. 323 00:16:17,230 --> 00:16:21,430 Two times-- oh, something weird happened to my pen. 324 00:16:21,430 --> 00:16:25,130 Two times four is exactly equal to eight. 325 00:16:25,130 --> 00:16:27,500 So two goes into eight four times. 326 00:16:27,500 --> 00:16:29,750 So I could say two goes into eight four times. 327 00:16:29,750 --> 00:16:33,200 Or eight divided by two is equal to four. 328 00:16:33,200 --> 00:16:35,030 We can even draw our circles. 329 00:16:35,030 --> 00:16:38,490 One, two, three, four, five, six, seven, eight. 330 00:16:38,490 --> 00:16:40,080 I drew them messy on purpose. 331 00:16:40,080 --> 00:16:42,950 Let's divide them into groups of two. 332 00:16:42,950 --> 00:16:47,240 I have one group of two, two groups of two, 333 00:16:47,240 --> 00:16:51,010 three groups of two, four groups of two. 334 00:16:51,010 --> 00:16:54,170 So if I have eight objects, divide them into groups of two, 335 00:16:54,170 --> 00:16:55,460 you have four groups. 336 00:16:55,460 --> 00:16:59,210 So eight divided by two is four. 337 00:16:59,210 --> 00:17:01,460 Hopefully you found that helpful!