0:00:00.000,0:00:00.510


0:00:00.510,0:00:04.640
Divide and write the answer[br]as a mixed number.

0:00:04.640,0:00:07.770
And we have 3/5 divided[br]by 1/2.

0:00:07.770,0:00:10.220
Now, whenever you're dividing[br]any fractions, you just have

0:00:10.220,0:00:14.200
to remember that dividing by a[br]fraction is the same thing as

0:00:14.200,0:00:16.970
multiplying by its reciprocal.

0:00:16.970,0:00:22.810
So this thing right here is the[br]same thing as 3/5 times--

0:00:22.810,0:00:25.780
so this is our 3/5 right here,[br]and instead of a division

0:00:25.780,0:00:28.120
sign, you want a multiplication[br]sign, and

0:00:28.120,0:00:31.880
instead of a 1/2, you want to[br]take the reciprocal of 1/2,

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which would be 2/1--[br]so times 2/1.

0:00:36.510,0:00:39.770
So dividing by 1/2 is the[br]exact same thing as

0:00:39.770,0:00:42.360
multiplying by 2/1.

0:00:42.360,0:00:45.000
And we just do this as a[br]straightforward multiplication

0:00:45.000,0:00:46.080
problem now.

0:00:46.080,0:00:49.840
3 times 2 is 6, so our[br]new numerator is 6.

0:00:49.840,0:00:52.950
5 times 1 is 5.

0:00:52.950,0:00:57.360
So 3/5 divided by 1/2 as an[br]improper fraction is 6/5.

0:00:57.360,0:01:01.220
Now, they want us to write[br]it as at mixed number.

0:01:01.220,0:01:04.450
So we divide the 5 into[br]the 6, figure out how

0:01:04.450,0:01:05.300
many times it goes.

0:01:05.300,0:01:07.530
That'll be the whole number[br]part of the mixed number.

0:01:07.530,0:01:10.290
And then whatever's left over[br]will be the remaining

0:01:10.290,0:01:13.620
numerator over 5.

0:01:13.620,0:01:18.160
So what we'll do is[br]take 5 into 6.

0:01:18.160,0:01:20.600
5 goes into 6 one time.

0:01:20.600,0:01:22.700
1 times 5 is 5.

0:01:22.700,0:01:23.360
Subtract.

0:01:23.360,0:01:25.960
You have a remainder of 1.

0:01:25.960,0:01:34.460
So 6/5 is equal to one whole,[br]or 5/5, and 1/5.

0:01:34.460,0:01:38.910


0:01:38.910,0:01:42.610
This 1 comes from whatever[br]is left over.

0:01:42.610,0:01:43.630
And now we're done!

0:01:43.630,0:01:46.730
3/5 divided by 1/2[br]is 1 and 1/5.

0:01:46.730,0:01:49.350
Now, the one thing that's not[br]obvious is why did this work?

0:01:49.350,0:01:53.660
Why is dividing by 1/2 the[br]same thing as multiplying

0:01:53.660,0:01:54.880
essentially by 2.

0:01:54.880,0:01:57.000
2/1 is the same thing as 2.

0:01:57.000,0:01:59.890
And to do that, I'll do a little[br]side-- fairly simple--

0:01:59.890,0:02:03.870
example, but hopefully, it[br]gets the point across.

0:02:03.870,0:02:05.910
Let me take four objects.

0:02:05.910,0:02:08.850
So we have four objects:[br]one, two, three, four.

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So I have four objects, and if[br]I were to divide into groups

0:02:13.790,0:02:17.300
of two, so I want to divide[br]it into groups of two.

0:02:17.300,0:02:21.210
So that is one group of two and[br]then that is another group

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of two, how many groups[br]do I have?

0:02:23.600,0:02:27.400
Well, 4 divided by 2, I have two[br]groups of two, so that is

0:02:27.400,0:02:28.900
equal to 2.

0:02:28.900,0:02:31.460
Now, what if I took those[br]same four objects:

0:02:31.460,0:02:33.990
one, two, three, four.

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So I'm taking those[br]same four objects.

0:02:36.160,0:02:38.890
Instead of dividing them into[br]groups of two, I want to

0:02:38.890,0:02:44.610
divide them into groups of 1/2,[br]which means each group

0:02:44.610,0:02:47.080
will have half of[br]an object in it.

0:02:47.080,0:02:49.960
So let's say that would be[br]one group right there.

0:02:49.960,0:02:51.900
That is a second group.

0:02:51.900,0:02:53.140
That is a third group.

0:02:53.140,0:02:56.690
I think you see each group has[br]half of a circle in it.

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That is the fourth.

0:02:58.280,0:03:00.070
That's the fifth.

0:03:00.070,0:03:01.390
That's the sixth.

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That's the seventh, and then[br]that's the eighth.

0:03:03.790,0:03:08.660
You have eight groups of 1/2,[br]so this is equal to 8.

0:03:08.660,0:03:12.920
And notice, now each of the[br]objects became two groups.

0:03:12.920,0:03:14.660
So you could say how many[br]groups do you have?

0:03:14.660,0:03:16.860
Well, you have four objects[br]and each of

0:03:16.860,0:03:21.290
them became two groups.

0:03:21.290,0:03:22.270
I'm looking for a[br]different color.

0:03:22.270,0:03:24.520
Each of them became[br]two groups, and so

0:03:24.520,0:03:26.840
you also have eight.

0:03:26.840,0:03:30.710
So dividing by 1/2 is the same[br]thing as multiplying by 2.

0:03:30.710,0:03:32.250
And you could think about it[br]with other numbers, but

0:03:32.250,0:03:35.020
hopefully, that gives you a[br]little bit of an intuition.

0:03:35.020,0:03:35.334