[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.73,0:00:04.27,Default,,0000,0000,0000,,I think you've probably heard the word divide before,
Dialogue: 0,0:00:04.27,0:00:06.73,Default,,0000,0000,0000,,where someone tells you to divide something up.
Dialogue: 0,0:00:06.73,0:00:10.45,Default,,0000,0000,0000,,Divide the money between you and your brother
Dialogue: 0,0:00:10.45,0:00:12.65,Default,,0000,0000,0000,,or between you and your buddy.
Dialogue: 0,0:00:12.65,0:00:14.64,Default,,0000,0000,0000,,And it essentially means to cut up something.
Dialogue: 0,0:00:14.64,0:00:20.46,Default,,0000,0000,0000,,So let me write down the word divide.
Dialogue: 0,0:00:20.46,0:00:24.33,Default,,0000,0000,0000,,Let's say that I have four quarters.
Dialogue: 0,0:00:24.33,0:00:27.50,Default,,0000,0000,0000,,Do my best to draw the quarters.
Dialogue: 0,0:00:27.50,0:00:32.32,Default,,0000,0000,0000,,If I have four quarters just like that.
Dialogue: 0,0:00:32.32,0:00:36.03,Default,,0000,0000,0000,,That's my rendition of George Washington on the quarters.
Dialogue: 0,0:00:36.03,0:00:37.62,Default,,0000,0000,0000,,And let's say there's two of us,
Dialogue: 0,0:00:37.62,0:00:40.55,Default,,0000,0000,0000,,and we're going to divide the quarters between us.
Dialogue: 0,0:00:40.55,0:00:42.52,Default,,0000,0000,0000,,So this is me right here.
Dialogue: 0,0:00:42.52,0:00:45.87,Default,,0000,0000,0000,,Let me try my best to draw me.
Dialogue: 0,0:00:45.87,0:00:48.76,Default,,0000,0000,0000,,So that's me right there.
Dialogue: 0,0:00:48.76,0:00:51.16,Default,,0000,0000,0000,,Let's see, I have a lot of hair.
Dialogue: 0,0:00:51.16,0:00:55.70,Default,,0000,0000,0000,,And then this is you right there.
Dialogue: 0,0:00:55.70,0:00:57.30,Default,,0000,0000,0000,,I'll do my best.
Dialogue: 0,0:00:57.30,0:00:59.27,Default,,0000,0000,0000,,Let's say you're bald.
Dialogue: 0,0:00:59.27,0:01:04.41,Default,,0000,0000,0000,,But you have side burns.
Dialogue: 0,0:01:04.41,0:01:09.08,Default,,0000,0000,0000,,Maybe you have a little bit of a beard.
Dialogue: 0,0:01:09.09,0:01:10.32,Default,,0000,0000,0000,,So that's you, that's me,
Dialogue: 0,0:01:10.32,0:01:15.52,Default,,0000,0000,0000,,and we're going to divide these four quarters between the two of us.
Dialogue: 0,0:01:15.52,0:01:20.88,Default,,0000,0000,0000,,So notice, we have four quarters
Dialogue: 0,0:01:20.88,0:01:23.58,Default,,0000,0000,0000,,and we're going to divide between the two of us.
Dialogue: 0,0:01:23.58,0:01:26.54,Default,,0000,0000,0000,,There are two of us.
Dialogue: 0,0:01:26.54,0:01:28.74,Default,,0000,0000,0000,,And I want to stress the number two.
Dialogue: 0,0:01:28.74,0:01:31.88,Default,,0000,0000,0000,,So we're going to divide four quarters by two.
Dialogue: 0,0:01:31.88,0:01:34.48,Default,,0000,0000,0000,,We're going to divide it between the two of us.
Dialogue: 0,0:01:34.48,0:01:36.90,Default,,0000,0000,0000,,And you've probably done something like this.
Dialogue: 0,0:01:36.90,0:01:37.54,Default,,0000,0000,0000,,What happens?
Dialogue: 0,0:01:37.54,0:01:40.23,Default,,0000,0000,0000,,Well, each of us are going to get two quarters.
Dialogue: 0,0:01:40.23,0:01:41.29,Default,,0000,0000,0000,,So let me divide it.
Dialogue: 0,0:01:41.29,0:01:43.18,Default,,0000,0000,0000,,We're going to divide it into two.
Dialogue: 0,0:01:43.18,0:01:46.06,Default,,0000,0000,0000,,Essentially what I did do is I take the four quarters
Dialogue: 0,0:01:46.08,0:01:48.95,Default,,0000,0000,0000,,and I divide it into two equal groups.
Dialogue: 0,0:01:48.95,0:01:51.70,Default,,0000,0000,0000,,Two equal groups.
Dialogue: 0,0:01:51.71,0:01:53.93,Default,,0000,0000,0000,,And that's what division is.
Dialogue: 0,0:01:53.93,0:01:57.62,Default,,0000,0000,0000,,We cut up this group of quarters into two equal groups.
Dialogue: 0,0:01:57.62,0:02:01.01,Default,,0000,0000,0000,,So when you divide four quarters into two groups,
Dialogue: 0,0:02:01.01,0:02:08.06,Default,,0000,0000,0000,,so this was four quarters right there.
Dialogue: 0,0:02:08.06,0:02:09.59,Default,,0000,0000,0000,,And you want to divide it into two groups.
Dialogue: 0,0:02:09.59,0:02:11.77,Default,,0000,0000,0000,,This is group one.
Dialogue: 0,0:02:11.77,0:02:16.53,Default,,0000,0000,0000,,Group one right here.
Dialogue: 0,0:02:16.53,0:02:19.38,Default,,0000,0000,0000,,And this is group two right here.
Dialogue: 0,0:02:19.38,0:02:21.89,Default,,0000,0000,0000,,How many numbers are in each group?
Dialogue: 0,0:02:21.89,0:02:23.99,Default,,0000,0000,0000,,Or how many quarters are in each group?
Dialogue: 0,0:02:23.99,0:02:26.87,Default,,0000,0000,0000,,Well, in each group I have one, two quarters.
Dialogue: 0,0:02:26.87,0:02:28.66,Default,,0000,0000,0000,,I'll need to use a brighter color.
Dialogue: 0,0:02:28.66,0:02:31.26,Default,,0000,0000,0000,,I have one, two quarters in each group.
Dialogue: 0,0:02:31.26,0:02:34.04,Default,,0000,0000,0000,,One quarter and two quarters in each group.
Dialogue: 0,0:02:34.04,0:02:36.15,Default,,0000,0000,0000,,So to write this out mathematically,
Dialogue: 0,0:02:36.15,0:02:37.86,Default,,0000,0000,0000,,I think this is something that you've done,
Dialogue: 0,0:02:37.86,0:02:40.73,Default,,0000,0000,0000,,probably as long as you've been splitting money
Dialogue: 0,0:02:40.73,0:02:42.88,Default,,0000,0000,0000,,between you and your siblings and your buddies.
Dialogue: 0,0:02:42.88,0:02:44.07,Default,,0000,0000,0000,,Actually, let me scroll over a little bit,
Dialogue: 0,0:02:44.07,0:02:47.33,Default,,0000,0000,0000,,so you can see my entire picture.
Dialogue: 0,0:02:47.33,0:02:50.36,Default,,0000,0000,0000,,How do we write this mathematically?
Dialogue: 0,0:02:50.36,0:02:55.27,Default,,0000,0000,0000,,We can write that four divided by-- so this four.
Dialogue: 0,0:02:55.27,0:02:56.98,Default,,0000,0000,0000,,Let me use the right colors.
Dialogue: 0,0:02:56.98,0:03:03.76,Default,,0000,0000,0000,,So this four, which is this four, divided by the two groups,
Dialogue: 0,0:03:03.76,0:03:07.50,Default,,0000,0000,0000,,these are the two groups: group one and this is group two right here.
Dialogue: 0,0:03:07.50,0:03:11.03,Default,,0000,0000,0000,,So divided into two groups or into two collections.
Dialogue: 0,0:03:11.03,0:03:14.95,Default,,0000,0000,0000,,Four divided by two is equal to--
Dialogue: 0,0:03:14.95,0:03:17.85,Default,,0000,0000,0000,,when you divide four into two groups,
Dialogue: 0,0:03:17.85,0:03:20.36,Default,,0000,0000,0000,,each group is going to have two quarters in it.
Dialogue: 0,0:03:20.36,0:03:22.92,Default,,0000,0000,0000,,It's going to be equal to two.
Dialogue: 0,0:03:22.92,0:03:24.39,Default,,0000,0000,0000,,And I just wanted to use this example
Dialogue: 0,0:03:24.39,0:03:25.15,Default,,0000,0000,0000,,because I want to show you
Dialogue: 0,0:03:25.15,0:03:29.26,Default,,0000,0000,0000,,that division is something that you've been using all along.
Dialogue: 0,0:03:29.26,0:03:32.82,Default,,0000,0000,0000,,And another important, I guess, takeaway or thing to realize about this,
Dialogue: 0,0:03:32.82,0:03:36.33,Default,,0000,0000,0000,,is on some level this is the opposite of multiplication.
Dialogue: 0,0:03:36.33,0:03:42.56,Default,,0000,0000,0000,,If I said that I had two groups of two quarters,
Dialogue: 0,0:03:42.56,0:03:48.69,Default,,0000,0000,0000,,I would multiply the two groups times the two quarters each
Dialogue: 0,0:03:48.69,0:03:52.85,Default,,0000,0000,0000,,and I would say I would then have four quarters.
Dialogue: 0,0:03:52.85,0:03:55.89,Default,,0000,0000,0000,,So on some level, these are saying the same thing.
Dialogue: 0,0:03:55.90,0:03:58.54,Default,,0000,0000,0000,,But just to make it a little bit more concrete in our head,
Dialogue: 0,0:03:58.54,0:04:01.40,Default,,0000,0000,0000,,let's do a couple of more examples.
Dialogue: 0,0:04:01.40,0:04:03.60,Default,,0000,0000,0000,,Let's do a bunch of more examples.
Dialogue: 0,0:04:03.60,0:04:08.68,Default,,0000,0000,0000,,So let's write down, what is six divided by--
Dialogue: 0,0:04:08.68,0:04:10.90,Default,,0000,0000,0000,,I'm trying to keep it nice and color coded.
Dialogue: 0,0:04:10.90,0:04:14.80,Default,,0000,0000,0000,,Six divided by three, what is that equal to?
Dialogue: 0,0:04:14.80,0:04:17.15,Default,,0000,0000,0000,,Let's just draw six objects.
Dialogue: 0,0:04:17.15,0:04:18.59,Default,,0000,0000,0000,,They can be anything.
Dialogue: 0,0:04:18.59,0:04:23.03,Default,,0000,0000,0000,,Let's say I have six bell peppers.
Dialogue: 0,0:04:23.03,0:04:25.05,Default,,0000,0000,0000,,I won't take too much trouble to draw them.
Dialogue: 0,0:04:25.05,0:04:27.26,Default,,0000,0000,0000,,Well, that's not what a bell pepper looks like,
Dialogue: 0,0:04:27.26,0:04:28.21,Default,,0000,0000,0000,,but you get the idea.
Dialogue: 0,0:04:28.21,0:04:34.37,Default,,0000,0000,0000,,So one, two, three, four, five, six.
Dialogue: 0,0:04:34.37,0:04:36.03,Default,,0000,0000,0000,,And I'm going to divide it by three.
Dialogue: 0,0:04:36.03,0:04:37.70,Default,,0000,0000,0000,,And one way that we can think about that
Dialogue: 0,0:04:37.70,0:04:41.06,Default,,0000,0000,0000,,is that means I want to divide my six bell peppers
Dialogue: 0,0:04:41.06,0:04:43.73,Default,,0000,0000,0000,,into three equal groups of bell peppers.
Dialogue: 0,0:04:43.73,0:04:47.38,Default,,0000,0000,0000,,You could kind of think of it as if three people are going to share these bell peppers,
Dialogue: 0,0:04:47.38,0:04:48.97,Default,,0000,0000,0000,,how many do each of them get?
Dialogue: 0,0:04:48.97,0:04:50.84,Default,,0000,0000,0000,,So let's divide it into three groups.
Dialogue: 0,0:04:50.84,0:04:52.77,Default,,0000,0000,0000,,So that's our six bell peppers.
Dialogue: 0,0:04:52.77,0:04:54.58,Default,,0000,0000,0000,,I'm going to divide it into three groups.
Dialogue: 0,0:04:54.58,0:04:56.56,Default,,0000,0000,0000,,So the best way to divide it into three groups is
Dialogue: 0,0:04:56.56,0:05:02.47,Default,,0000,0000,0000,,I can have one group right there, two groups, or the second group right there,
Dialogue: 0,0:05:02.47,0:05:04.91,Default,,0000,0000,0000,,and then, the third group.
Dialogue: 0,0:05:04.91,0:05:10.35,Default,,0000,0000,0000,,And then each group will have exactly how many bell peppers?
Dialogue: 0,0:05:10.35,0:05:12.12,Default,,0000,0000,0000,,They'll have one, two.
Dialogue: 0,0:05:12.12,0:05:13.51,Default,,0000,0000,0000,,One, two.
Dialogue: 0,0:05:13.51,0:05:15.14,Default,,0000,0000,0000,,One, two bell peppers.
Dialogue: 0,0:05:15.14,0:05:20.06,Default,,0000,0000,0000,,So six divided by three is equal to two.
Dialogue: 0,0:05:20.06,0:05:22.38,Default,,0000,0000,0000,,So the best way or one way to think about it
Dialogue: 0,0:05:22.38,0:05:26.79,Default,,0000,0000,0000,,is that you divided the six into three groups.
Dialogue: 0,0:05:26.79,0:05:29.88,Default,,0000,0000,0000,,Now you could view that a slightly different way,
Dialogue: 0,0:05:29.88,0:05:31.39,Default,,0000,0000,0000,,although it's not completely different,
Dialogue: 0,0:05:31.39,0:05:33.11,Default,,0000,0000,0000,,but it's a good way to think about it.
Dialogue: 0,0:05:33.11,0:05:38.15,Default,,0000,0000,0000,,You could also think of it as six divided by three.
Dialogue: 0,0:05:38.15,0:05:42.94,Default,,0000,0000,0000,,And once again, let's say I have raspberries now-- easier to draw.
Dialogue: 0,0:05:42.95,0:05:47.46,Default,,0000,0000,0000,,One, two, three, four, five, six.
Dialogue: 0,0:05:47.46,0:05:51.60,Default,,0000,0000,0000,,And here, instead of dividing it into three groups like we did here.
Dialogue: 0,0:05:51.60,0:05:54.29,Default,,0000,0000,0000,,This was one group, two group, three groups.
Dialogue: 0,0:05:54.29,0:05:56.16,Default,,0000,0000,0000,,Instead of dividing into three groups,
Dialogue: 0,0:05:56.16,0:05:57.52,Default,,0000,0000,0000,,what I want to do is say well,
Dialogue: 0,0:05:57.52,0:06:02.71,Default,,0000,0000,0000,,if I'm dividing six divided by three, I want to divide it into groups of three.
Dialogue: 0,0:06:02.71,0:06:04.26,Default,,0000,0000,0000,,Not into three groups.
Dialogue: 0,0:06:04.26,0:06:05.96,Default,,0000,0000,0000,,I want to divide it into groups of three.
Dialogue: 0,0:06:05.96,0:06:09.49,Default,,0000,0000,0000,,So how many groups of three am I going to have?
Dialogue: 0,0:06:09.49,0:06:12.93,Default,,0000,0000,0000,,Well, let me draw some groups of three.
Dialogue: 0,0:06:12.93,0:06:16.04,Default,,0000,0000,0000,,So that is one group of three.
Dialogue: 0,0:06:16.04,0:06:21.72,Default,,0000,0000,0000,,And that is two groups of three.
Dialogue: 0,0:06:21.72,0:06:26.67,Default,,0000,0000,0000,,So if I take six things and I divide them into groups of three,
Dialogue: 0,0:06:26.67,0:06:29.95,Default,,0000,0000,0000,,I will end up with one, two groups.
Dialogue: 0,0:06:29.95,0:06:33.23,Default,,0000,0000,0000,,So that's another way to think about division.
Dialogue: 0,0:06:33.23,0:06:34.55,Default,,0000,0000,0000,,And this is an interesting thing.
Dialogue: 0,0:06:34.55,0:06:36.91,Default,,0000,0000,0000,,When you think about these two relations,
Dialogue: 0,0:06:36.91,0:06:42.12,Default,,0000,0000,0000,,you'll see a relationship between six divided by three and six divided by two.
Dialogue: 0,0:06:42.12,0:06:43.72,Default,,0000,0000,0000,,Let me do that right here.
Dialogue: 0,0:06:43.72,0:06:48.48,Default,,0000,0000,0000,,What is six divided by two,
Dialogue: 0,0:06:48.48,0:06:51.74,Default,,0000,0000,0000,,when you think of it in this context right here?
Dialogue: 0,0:06:51.74,0:06:54.85,Default,,0000,0000,0000,,Six divided by two, when you do it like that--
Dialogue: 0,0:06:54.85,0:06:58.78,Default,,0000,0000,0000,,let me draw one, two, three, four, five, six.
Dialogue: 0,0:06:58.78,0:07:03.29,Default,,0000,0000,0000,,When we think about six divided by two in terms of dividing it into two groups,
Dialogue: 0,0:07:03.29,0:07:06.72,Default,,0000,0000,0000,,what we can end up is we could have one group like this
Dialogue: 0,0:07:06.72,0:07:08.67,Default,,0000,0000,0000,,and then one group like this,
Dialogue: 0,0:07:08.67,0:07:11.50,Default,,0000,0000,0000,,and each group will have three elements.
Dialogue: 0,0:07:11.50,0:07:12.54,Default,,0000,0000,0000,,It'll have three things in it.
Dialogue: 0,0:07:12.54,0:07:14.73,Default,,0000,0000,0000,,So six divided by two is three.
Dialogue: 0,0:07:14.73,0:07:16.40,Default,,0000,0000,0000,,Or you could think of it the other way.
Dialogue: 0,0:07:16.40,0:07:21.68,Default,,0000,0000,0000,,You could say that six divided by two is--
Dialogue: 0,0:07:21.68,0:07:26.42,Default,,0000,0000,0000,,you're taking six objects: one, two, three, four, five, six.
Dialogue: 0,0:07:26.42,0:07:29.04,Default,,0000,0000,0000,,And your dividing it into groups of two
Dialogue: 0,0:07:29.04,0:07:31.20,Default,,0000,0000,0000,,where each group has two elements.
Dialogue: 0,0:07:31.20,0:07:32.92,Default,,0000,0000,0000,,And that on some level is an easier thing to do.
Dialogue: 0,0:07:32.92,0:07:36.64,Default,,0000,0000,0000,,If each group has two elements, well, that's the one right there.
Dialogue: 0,0:07:36.64,0:07:38.69,Default,,0000,0000,0000,,They don't even have to be nicely ordered.
Dialogue: 0,0:07:38.69,0:07:40.90,Default,,0000,0000,0000,,This could be one group right there
Dialogue: 0,0:07:40.90,0:07:42.99,Default,,0000,0000,0000,,and that could be the other group right there.
Dialogue: 0,0:07:42.99,0:07:44.58,Default,,0000,0000,0000,,I don't have to draw them all stacked up.
Dialogue: 0,0:07:44.58,0:07:45.92,Default,,0000,0000,0000,,These are just groups of two.
Dialogue: 0,0:07:45.92,0:07:47.39,Default,,0000,0000,0000,,But how many groups do I have?
Dialogue: 0,0:07:47.39,0:07:49.25,Default,,0000,0000,0000,,I have one, two, three.
Dialogue: 0,0:07:49.25,0:07:51.07,Default,,0000,0000,0000,,I have three groups.
Dialogue: 0,0:07:51.07,0:07:57.71,Default,,0000,0000,0000,,But notice something, it's no coincidence that six divided by three is two,
Dialogue: 0,0:07:57.71,0:08:00.69,Default,,0000,0000,0000,,and six divided by two is three.
Dialogue: 0,0:08:00.69,0:08:03.28,Default,,0000,0000,0000,,Let me write that down.
Dialogue: 0,0:08:03.28,0:08:08.72,Default,,0000,0000,0000,,We get six divided by three is equal to two,
Dialogue: 0,0:08:08.72,0:08:13.29,Default,,0000,0000,0000,,and six divided by two is equal to three.
Dialogue: 0,0:08:13.29,0:08:19.51,Default,,0000,0000,0000,,And the reason why you see this relation where you can kind of swap this two and this three
Dialogue: 0,0:08:19.51,0:08:26.12,Default,,0000,0000,0000,,is because two times three is equal to six.
Dialogue: 0,0:08:26.12,0:08:28.48,Default,,0000,0000,0000,,Let's say I have two groups of three.
Dialogue: 0,0:08:28.49,0:08:29.84,Default,,0000,0000,0000,,Let me draw two groups of three.
Dialogue: 0,0:08:29.84,0:08:37.29,Default,,0000,0000,0000,,So that's one group of three and then here's another group of three.
Dialogue: 0,0:08:37.29,0:08:40.79,Default,,0000,0000,0000,,So two groups of three is equal to six.
Dialogue: 0,0:08:40.79,0:08:44.36,Default,,0000,0000,0000,,Two times three is equal to six.
Dialogue: 0,0:08:44.36,0:08:46.40,Default,,0000,0000,0000,,Or you could think of it the other way,
Dialogue: 0,0:08:46.40,0:08:48.09,Default,,0000,0000,0000,,if I have three groups of two.
Dialogue: 0,0:08:48.09,0:08:50.90,Default,,0000,0000,0000,,So that's one group of two right there.
Dialogue: 0,0:08:50.90,0:08:53.84,Default,,0000,0000,0000,,I have another group of two right there.
Dialogue: 0,0:08:53.84,0:08:56.45,Default,,0000,0000,0000,,And then I have a third group of two right there.
Dialogue: 0,0:08:56.45,0:08:57.96,Default,,0000,0000,0000,,What is that equal to?
Dialogue: 0,0:08:57.96,0:09:01.24,Default,,0000,0000,0000,,Three groups of two-- three times two.
Dialogue: 0,0:09:01.24,0:09:03.26,Default,,0000,0000,0000,,That's also equal to six.
Dialogue: 0,0:09:03.26,0:09:04.84,Default,,0000,0000,0000,,So two times three is equal to six.
Dialogue: 0,0:09:04.84,0:09:05.97,Default,,0000,0000,0000,,Three times two is equal to six.
Dialogue: 0,0:09:05.97,0:09:07.52,Default,,0000,0000,0000,,We saw this in the multiplication video
Dialogue: 0,0:09:07.52,0:09:09.53,Default,,0000,0000,0000,,that the order doesn't matter.
Dialogue: 0,0:09:09.53,0:09:12.18,Default,,0000,0000,0000,,But that's the reason why if you want to divide it,
Dialogue: 0,0:09:12.18,0:09:13.37,Default,,0000,0000,0000,,if you want to go the other way--
Dialogue: 0,0:09:13.37,0:09:18.99,Default,,0000,0000,0000,,if you have six things and you want to divide it into groups of two, you get three.
Dialogue: 0,0:09:18.99,0:09:23.06,Default,,0000,0000,0000,,If you have six and you want to divide into groups of three, you get two.
Dialogue: 0,0:09:23.07,0:09:24.36,Default,,0000,0000,0000,,Let's do a couple more problems.
Dialogue: 0,0:09:24.36,0:09:33.96,Default,,0000,0000,0000,,I think it'll really make sense about what division is all about.
Dialogue: 0,0:09:33.96,0:09:35.86,Default,,0000,0000,0000,,Let's do an interesting one.
Dialogue: 0,0:09:35.87,0:09:40.60,Default,,0000,0000,0000,,Let's do nine divided by four.
Dialogue: 0,0:09:40.60,0:09:43.36,Default,,0000,0000,0000,,So if we think about nine divided by four, let me draw nine objects.
Dialogue: 0,0:09:43.36,0:09:51.17,Default,,0000,0000,0000,,One, two, three, four, five, six, seven, eight, nine.
Dialogue: 0,0:09:51.17,0:09:54.11,Default,,0000,0000,0000,,Now when you divide by four, for this problem,
Dialogue: 0,0:09:54.11,0:09:57.14,Default,,0000,0000,0000,,I'm thinking about dividing it into groups of four.
Dialogue: 0,0:09:57.14,0:09:58.92,Default,,0000,0000,0000,,So if I want to divide it into groups of four--
Dialogue: 0,0:09:58.92,0:09:59.90,Default,,0000,0000,0000,,Let me try doing that.
Dialogue: 0,0:09:59.90,0:10:02.52,Default,,0000,0000,0000,,So here is one group of four.
Dialogue: 0,0:10:02.52,0:10:04.82,Default,,0000,0000,0000,,I just picked any of them right like that.
Dialogue: 0,0:10:04.82,0:10:06.57,Default,,0000,0000,0000,,That's one group of four.
Dialogue: 0,0:10:06.57,0:10:11.10,Default,,0000,0000,0000,,Then here's another group of four, right there.
Dialogue: 0,0:10:11.10,0:10:13.33,Default,,0000,0000,0000,,And then I have this left over thing.
Dialogue: 0,0:10:13.33,0:10:15.05,Default,,0000,0000,0000,,Maybe we could call it a remainder,
Dialogue: 0,0:10:15.05,0:10:18.24,Default,,0000,0000,0000,,where I can't put this one into a group of four.
Dialogue: 0,0:10:18.24,0:10:20.79,Default,,0000,0000,0000,,When I'm dividing by four,
Dialogue: 0,0:10:20.79,0:10:24.09,Default,,0000,0000,0000,,I can only cut up the nine into groups of four.
Dialogue: 0,0:10:24.09,0:10:28.10,Default,,0000,0000,0000,,So the answer here, and this is a new concept for you maybe,
Dialogue: 0,0:10:28.10,0:10:32.40,Default,,0000,0000,0000,,nine divided by four is going to be two groups.
Dialogue: 0,0:10:32.40,0:10:34.80,Default,,0000,0000,0000,,I have one group here, and another group here,
Dialogue: 0,0:10:34.80,0:10:36.67,Default,,0000,0000,0000,,and then I have a remainder of one.
Dialogue: 0,0:10:36.67,0:10:38.97,Default,,0000,0000,0000,,I have one left over that I wasn't able to do with.
Dialogue: 0,0:10:38.97,0:10:45.87,Default,,0000,0000,0000,,Remainder-- that says remainder one.
Dialogue: 0,0:10:45.89,0:10:49.35,Default,,0000,0000,0000,,Nine divided by four is two remainder one.
Dialogue: 0,0:10:49.35,0:10:53.01,Default,,0000,0000,0000,,If I asked you what twelve divided by four is-- so let me do twelve.
Dialogue: 0,0:10:53.01,0:11:00.80,Default,,0000,0000,0000,,One, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve.
Dialogue: 0,0:11:00.80,0:11:01.98,Default,,0000,0000,0000,,So let me write that down.
Dialogue: 0,0:11:01.98,0:11:05.92,Default,,0000,0000,0000,,Twelve divided by four.
Dialogue: 0,0:11:05.92,0:11:08.41,Default,,0000,0000,0000,,So I want to divide these twelve objects--
Dialogue: 0,0:11:08.41,0:11:10.48,Default,,0000,0000,0000,,maybe they're apples or plums.
Dialogue: 0,0:11:10.48,0:11:12.90,Default,,0000,0000,0000,,And divide them into groups of four.
Dialogue: 0,0:11:12.90,0:11:14.84,Default,,0000,0000,0000,,So let me see if I can do that.
Dialogue: 0,0:11:14.84,0:11:19.34,Default,,0000,0000,0000,,So this is one group of four just like that.
Dialogue: 0,0:11:19.34,0:11:23.34,Default,,0000,0000,0000,,This is another group of four just like that.
Dialogue: 0,0:11:23.34,0:11:24.19,Default,,0000,0000,0000,,And this is pretty straightforward.
Dialogue: 0,0:11:24.19,0:11:26.67,Default,,0000,0000,0000,,And then I have a third group of four.
Dialogue: 0,0:11:26.67,0:11:27.100,Default,,0000,0000,0000,,Just like that.
Dialogue: 0,0:11:27.100,0:11:30.75,Default,,0000,0000,0000,,And there's nothing left over, like I had before.
Dialogue: 0,0:11:30.75,0:11:35.21,Default,,0000,0000,0000,,I can exactly divide twelve objects into three groups of four.
Dialogue: 0,0:11:35.21,0:11:38.19,Default,,0000,0000,0000,,One, two, three groups of four.
Dialogue: 0,0:11:38.19,0:11:44.47,Default,,0000,0000,0000,,So twelve divided by four is equal to three.
Dialogue: 0,0:11:44.47,0:11:47.11,Default,,0000,0000,0000,,And we can do the exercise that we saw on the previous video.
Dialogue: 0,0:11:47.11,0:11:49.67,Default,,0000,0000,0000,,What is twelve divided by three?
Dialogue: 0,0:11:49.67,0:11:51.84,Default,,0000,0000,0000,,Let me do a new color.
Dialogue: 0,0:11:51.84,0:11:55.20,Default,,0000,0000,0000,,Twelve divided by three.
Dialogue: 0,0:11:55.20,0:11:56.50,Default,,0000,0000,0000,,Now based on what we've learn so far,
Dialogue: 0,0:11:56.50,0:12:00.88,Default,,0000,0000,0000,,we say, that should just be four, because three times four is twelve.
Dialogue: 0,0:12:00.88,0:12:02.77,Default,,0000,0000,0000,,But let's prove it to ourselves.
Dialogue: 0,0:12:02.77,0:12:09.42,Default,,0000,0000,0000,,So one, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve.
Dialogue: 0,0:12:09.42,0:12:12.18,Default,,0000,0000,0000,,Let's divide it into groups of three.
Dialogue: 0,0:12:12.18,0:12:13.89,Default,,0000,0000,0000,,And I'm going to make them a little strange looking
Dialogue: 0,0:12:13.89,0:12:17.73,Default,,0000,0000,0000,,just so you see that you don't always have to do it into nice, clean columns.
Dialogue: 0,0:12:17.73,0:12:19.87,Default,,0000,0000,0000,,So that's a group of three, right there.
Dialogue: 0,0:12:19.87,0:12:21.68,Default,,0000,0000,0000,,Twelve divided by three.
Dialogue: 0,0:12:21.68,0:12:27.72,Default,,0000,0000,0000,,Let's see, here is another group of three just like that.
Dialogue: 0,0:12:27.72,0:12:33.01,Default,,0000,0000,0000,,And then, maybe I'll take this group of three like that.
Dialogue: 0,0:12:33.01,0:12:34.33,Default,,0000,0000,0000,,And I'll take this group of three.
Dialogue: 0,0:12:34.33,0:12:37.06,Default,,0000,0000,0000,,There was obviously a much easier way of dividing it up
Dialogue: 0,0:12:37.06,0:12:38.68,Default,,0000,0000,0000,,than doing these weird l-shaped things,
Dialogue: 0,0:12:38.68,0:12:40.11,Default,,0000,0000,0000,,but I want to show you it doesn't matter.
Dialogue: 0,0:12:40.11,0:12:42.10,Default,,0000,0000,0000,,You're just dividing it into groups of three.
Dialogue: 0,0:12:42.10,0:12:43.78,Default,,0000,0000,0000,,And how many groups do we have?
Dialogue: 0,0:12:43.78,0:12:45.55,Default,,0000,0000,0000,,We have one group.
Dialogue: 0,0:12:45.55,0:12:49.84,Default,,0000,0000,0000,,Then we have our second group right here.
Dialogue: 0,0:12:49.84,0:12:53.45,Default,,0000,0000,0000,,And then we have our third group right there.
Dialogue: 0,0:12:53.45,0:12:56.61,Default,,0000,0000,0000,,And then we have-- let me do it in a new color.
Dialogue: 0,0:12:56.61,0:12:59.11,Default,,0000,0000,0000,,And then we have our fourth group right there.
Dialogue: 0,0:12:59.11,0:13:01.90,Default,,0000,0000,0000,,So we have exactly four groups.
Dialogue: 0,0:13:01.90,0:13:03.69,Default,,0000,0000,0000,,And when I say there was an easier way to divide it,
Dialogue: 0,0:13:03.69,0:13:08.38,Default,,0000,0000,0000,,the easier way was obviously-- maybe not obviously--
Dialogue: 0,0:13:08.38,0:13:10.69,Default,,0000,0000,0000,,if I want to divide these into groups of three,
Dialogue: 0,0:13:10.69,0:13:16.74,Default,,0000,0000,0000,,I could have just done one, two, three, four groups of three.
Dialogue: 0,0:13:16.74,0:13:20.71,Default,,0000,0000,0000,,Either of these, I'm dividing the twelve objects into packets of three.
Dialogue: 0,0:13:20.71,0:13:21.79,Default,,0000,0000,0000,,You can imagine them that way.
Dialogue: 0,0:13:21.79,0:13:26.11,Default,,0000,0000,0000,,Let's do another one that maybe has a remainder.
Dialogue: 0,0:13:26.11,0:13:26.97,Default,,0000,0000,0000,,Let's see.
Dialogue: 0,0:13:26.98,0:13:36.35,Default,,0000,0000,0000,,What is fourteen divided by five?
Dialogue: 0,0:13:36.35,0:13:39.58,Default,,0000,0000,0000,,So let's draw fourteen objects.
Dialogue: 0,0:13:39.58,0:13:47.39,Default,,0000,0000,0000,,One, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve, thirteen, fourteen.
Dialogue: 0,0:13:47.39,0:13:48.33,Default,,0000,0000,0000,,Fourteen objects.
Dialogue: 0,0:13:48.33,0:13:51.85,Default,,0000,0000,0000,,And I'm going to divide it into groups of five.
Dialogue: 0,0:13:51.85,0:13:55.51,Default,,0000,0000,0000,,Well, the easiest thing is there's one group right there,
Dialogue: 0,0:13:55.51,0:13:57.93,Default,,0000,0000,0000,,two groups right there.
Dialogue: 0,0:13:57.93,0:13:59.92,Default,,0000,0000,0000,,But then this last one, I only have four left,
Dialogue: 0,0:13:59.92,0:14:01.99,Default,,0000,0000,0000,,so I can't make another group of five.
Dialogue: 0,0:14:01.99,0:14:05.43,Default,,0000,0000,0000,,So the answer here is I can make two groups of five,
Dialogue: 0,0:14:05.43,0:14:10.07,Default,,0000,0000,0000,,and I'm going to have a remainder-- r for remainder-- of four.
Dialogue: 0,0:14:10.07,0:14:11.68,Default,,0000,0000,0000,,Two remainder four.
Dialogue: 0,0:14:11.68,0:14:14.50,Default,,0000,0000,0000,,Now, once you get enough practice,
Dialogue: 0,0:14:14.50,0:14:16.87,Default,,0000,0000,0000,,you're not always going to be wanting to draw these circles
Dialogue: 0,0:14:16.87,0:14:18.27,Default,,0000,0000,0000,,and dividing them up like that.
Dialogue: 0,0:14:18.27,0:14:20.66,Default,,0000,0000,0000,,Although that would not be incorrect.
Dialogue: 0,0:14:20.66,0:14:23.40,Default,,0000,0000,0000,,So another way to think about this type of problem
Dialogue: 0,0:14:23.40,0:14:27.62,Default,,0000,0000,0000,,is to say, well, fourteen divided by five, how do I figure that out?
Dialogue: 0,0:14:27.62,0:14:28.70,Default,,0000,0000,0000,,Actually, another way of writing this,
Dialogue: 0,0:14:28.70,0:14:31.12,Default,,0000,0000,0000,,and no harm in showing you :
Dialogue: 0,0:14:31.12,0:14:36.03,Default,,0000,0000,0000,,I could say fourteen divided by five is the same thing as fourteen divided by--
Dialogue: 0,0:14:36.03,0:14:38.50,Default,,0000,0000,0000,,this sign right here-- divided by five.
Dialogue: 0,0:14:38.50,0:14:40.06,Default,,0000,0000,0000,,And what you do is you say, well, let's see.
Dialogue: 0,0:14:40.06,0:14:42.75,Default,,0000,0000,0000,,How many times does five go into fourteen?
Dialogue: 0,0:14:42.75,0:14:43.36,Default,,0000,0000,0000,,Well, let's see.
Dialogue: 0,0:14:43.36,0:14:45.97,Default,,0000,0000,0000,,Five times-- and you kind of do multiplication tables in your head--
Dialogue: 0,0:14:45.97,0:14:48.95,Default,,0000,0000,0000,,Five times one is equal to five.
Dialogue: 0,0:14:48.95,0:14:51.86,Default,,0000,0000,0000,,Five times two is equal to ten.
Dialogue: 0,0:14:51.86,0:14:55.96,Default,,0000,0000,0000,,So that's still less than fourteen, so five goes at least two times.
Dialogue: 0,0:14:55.96,0:14:59.14,Default,,0000,0000,0000,,Five times three is equal to fifteen.
Dialogue: 0,0:14:59.14,0:15:01.65,Default,,0000,0000,0000,,Well that's bigger than fourteen, so I have to go back here.
Dialogue: 0,0:15:01.65,0:15:03.98,Default,,0000,0000,0000,,So five only goes two times.
Dialogue: 0,0:15:03.98,0:15:05.63,Default,,0000,0000,0000,,So it goes two times.
Dialogue: 0,0:15:05.63,0:15:08.53,Default,,0000,0000,0000,,Two times five is ten.
Dialogue: 0,0:15:08.53,0:15:09.69,Default,,0000,0000,0000,,And then you subtract.
Dialogue: 0,0:15:09.69,0:15:12.16,Default,,0000,0000,0000,,You say fourteen minus ten is four.
Dialogue: 0,0:15:12.16,0:15:15.09,Default,,0000,0000,0000,,And that's the same remainder as right here.
Dialogue: 0,0:15:15.09,0:15:17.92,Default,,0000,0000,0000,,Well, I could divide five into fourteen exactly two times,
Dialogue: 0,0:15:17.92,0:15:19.58,Default,,0000,0000,0000,,which would get us two groups of five.
Dialogue: 0,0:15:19.58,0:15:21.09,Default,,0000,0000,0000,,Which is essentially just ten.
Dialogue: 0,0:15:21.09,0:15:28.09,Default,,0000,0000,0000,,And we still have the four left over.
Dialogue: 0,0:15:28.09,0:15:28.86,Default,,0000,0000,0000,,Let me do a couple of more,
Dialogue: 0,0:15:28.86,0:15:35.76,Default,,0000,0000,0000,,just to really make sure you get this stuff really, really, really, really well.
Dialogue: 0,0:15:35.76,0:15:37.54,Default,,0000,0000,0000,,Let me write it in that notation.
Dialogue: 0,0:15:37.54,0:15:41.66,Default,,0000,0000,0000,,Let's say I do eight divided by two.
Dialogue: 0,0:15:41.66,0:15:43.60,Default,,0000,0000,0000,,And I could also write this as eight--
Dialogue: 0,0:15:43.60,0:15:45.53,Default,,0000,0000,0000,,so I want to know what that is.
Dialogue: 0,0:15:45.53,0:15:46.79,Default,,0000,0000,0000,,That's a question mark.
Dialogue: 0,0:15:46.79,0:15:52.10,Default,,0000,0000,0000,,I could also write this as eight divided by two.
Dialogue: 0,0:15:52.10,0:15:55.02,Default,,0000,0000,0000,,And the way I do either of these-- I'll draw the circles in a second--
Dialogue: 0,0:15:55.02,0:15:57.66,Default,,0000,0000,0000,,but the way I do it without drawing the circles,
Dialogue: 0,0:15:57.66,0:16:01.22,Default,,0000,0000,0000,,I say, well, two times one is equal to two.
Dialogue: 0,0:16:01.22,0:16:02.68,Default,,0000,0000,0000,,So that definitely goes into eight,
Dialogue: 0,0:16:02.68,0:16:06.06,Default,,0000,0000,0000,,but maybe I can think of a larger number that goes into--
Dialogue: 0,0:16:06.06,0:16:09.07,Default,,0000,0000,0000,,that when I multiply it by two still goes into eight.
Dialogue: 0,0:16:09.07,0:16:11.36,Default,,0000,0000,0000,,Two times two is equal to four.
Dialogue: 0,0:16:11.36,0:16:13.07,Default,,0000,0000,0000,,That's still less than eight.
Dialogue: 0,0:16:13.07,0:16:15.71,Default,,0000,0000,0000,,So two times three is equal to six.
Dialogue: 0,0:16:15.71,0:16:17.23,Default,,0000,0000,0000,,Still less than eight.
Dialogue: 0,0:16:17.23,0:16:21.43,Default,,0000,0000,0000,,Two times-- oh, something weird happened to my pen.
Dialogue: 0,0:16:21.43,0:16:25.13,Default,,0000,0000,0000,,Two times four is exactly equal to eight.
Dialogue: 0,0:16:25.13,0:16:27.50,Default,,0000,0000,0000,,So two goes into eight four times.
Dialogue: 0,0:16:27.50,0:16:29.75,Default,,0000,0000,0000,,So I could say two goes into eight four times.
Dialogue: 0,0:16:29.75,0:16:33.20,Default,,0000,0000,0000,,Or eight divided by two is equal to four.
Dialogue: 0,0:16:33.20,0:16:35.03,Default,,0000,0000,0000,,We can even draw our circles.
Dialogue: 0,0:16:35.03,0:16:38.49,Default,,0000,0000,0000,,One, two, three, four, five, six, seven, eight.
Dialogue: 0,0:16:38.49,0:16:40.08,Default,,0000,0000,0000,,I drew them messy on purpose.
Dialogue: 0,0:16:40.08,0:16:42.95,Default,,0000,0000,0000,,Let's divide them into groups of two.
Dialogue: 0,0:16:42.95,0:16:47.24,Default,,0000,0000,0000,,I have one group of two, two groups of two,
Dialogue: 0,0:16:47.24,0:16:51.01,Default,,0000,0000,0000,,three groups of two, four groups of two.
Dialogue: 0,0:16:51.01,0:16:54.17,Default,,0000,0000,0000,,So if I have eight objects, divide them into groups of two,
Dialogue: 0,0:16:54.17,0:16:55.46,Default,,0000,0000,0000,,you have four groups.
Dialogue: 0,0:16:55.46,0:16:59.21,Default,,0000,0000,0000,,So eight divided by two is four.
Dialogue: 0,0:16:59.21,0:17:01.46,Default,,0000,0000,0000,,Hopefully you found that helpful!