1
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2
00:00:00,510 --> 00:00:04,639
Divide and write the answer as a mixed number.

3
00:00:04,639 --> 00:00:07,769
And we have 3/5 divided by 1/2.

4
00:00:07,769 --> 00:00:10,219
Now, whenever you're dividing any fractions, you just have

5
00:00:10,220 --> 00:00:14,200
to remember that dividing by a fraction is the same thing as

6
00:00:14,199 --> 00:00:16,969
multiplying by its reciprocal.

7
00:00:16,969 --> 00:00:22,809
So this thing right here is the same thing as 3/5 times--

8
00:00:22,809 --> 00:00:25,779
so this is our 3/5 right here, and instead of a division

9
00:00:25,780 --> 00:00:28,120
sign, you want a multiplication sign, and

10
00:00:28,120 --> 00:00:31,880
instead of a 1/2, you want to take the reciprocal of 1/2,

11
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which would be 2/1-- so times 2/1.

12
00:00:36,509 --> 00:00:39,769
So dividing by 1/2 is the exact same thing as

13
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multiplying by 2/1.

14
00:00:42,359 --> 00:00:45,000
And we just do this as a straightforward multiplication

15
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problem now.

16
00:00:46,079 --> 00:00:49,839
3 times 2 is 6, so our new numerator is 6.

17
00:00:49,840 --> 00:00:52,950
5 times 1 is 5.

18
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So 3/5 divided by 1/2 as an improper fraction is 6/5.

19
00:00:57,359 --> 00:01:01,219
Now, they want us to write it as at mixed number.

20
00:01:01,219 --> 00:01:04,450
So we divide the 5 into the 6, figure out how

21
00:01:04,450 --> 00:01:05,299
many times it goes.

22
00:01:05,299 --> 00:01:07,530
That'll be the whole number part of the mixed number.

23
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And then whatever's left over will be the remaining

24
00:01:10,290 --> 00:01:13,620
numerator over 5.

25
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So what we'll do is take 5 into 6.

26
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5 goes into 6 one time.

27
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1 times 5 is 5.

28
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Subtract.

29
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You have a remainder of 1.

30
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So 6/5 is equal to one whole, or 5/5, and 1/5.

31
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32
00:01:38,909 --> 00:01:42,609
This 1 comes from whatever is left over.

33
00:01:42,609 --> 00:01:43,629
And now we're done!

34
00:01:43,629 --> 00:01:46,729
3/5 divided by 1/2 is 1 and 1/5.

35
00:01:46,730 --> 00:01:49,350
Now, the one thing that's not obvious is why did this work?

36
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Why is dividing by 1/2 the same thing as multiplying

37
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essentially by 2.

38
00:01:54,879 --> 00:01:57,000
2/1 is the same thing as 2.

39
00:01:57,000 --> 00:01:59,890
And to do that, I'll do a little side-- fairly simple--

40
00:01:59,890 --> 00:02:03,870
example, but hopefully, it gets the point across.

41
00:02:03,870 --> 00:02:05,910
Let me take four objects.

42
00:02:05,909 --> 00:02:08,849
So we have four objects: one, two, three, four.

43
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So I have four objects, and if I were to divide into groups

44
00:02:13,789 --> 00:02:17,299
of two, so I want to divide it into groups of two.

45
00:02:17,300 --> 00:02:21,210
So that is one group of two and then that is another group

46
00:02:21,210 --> 00:02:23,599
of two, how many groups do I have?

47
00:02:23,599 --> 00:02:27,400
Well, 4 divided by 2, I have two groups of two, so that is

48
00:02:27,400 --> 00:02:28,900
equal to 2.

49
00:02:28,900 --> 00:02:31,460
Now, what if I took those same four objects:

50
00:02:31,460 --> 00:02:33,990
one, two, three, four.

51
00:02:33,990 --> 00:02:36,159
So I'm taking those same four objects.

52
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Instead of dividing them into groups of two, I want to

53
00:02:38,889 --> 00:02:44,609
divide them into groups of 1/2, which means each group

54
00:02:44,610 --> 00:02:47,080
will have half of an object in it.

55
00:02:47,080 --> 00:02:49,960
So let's say that would be one group right there.

56
00:02:49,960 --> 00:02:51,900
That is a second group.

57
00:02:51,900 --> 00:02:53,140
That is a third group.

58
00:02:53,139 --> 00:02:56,689
I think you see each group has half of a circle in it.

59
00:02:56,689 --> 00:02:58,280
That is the fourth.

60
00:02:58,280 --> 00:03:00,069
That's the fifth.

61
00:03:00,069 --> 00:03:01,389
That's the sixth.

62
00:03:01,389 --> 00:03:03,789
That's the seventh, and then that's the eighth.

63
00:03:03,789 --> 00:03:08,659
You have eight groups of 1/2, so this is equal to 8.

64
00:03:08,659 --> 00:03:12,919
And notice, now each of the objects became two groups.

65
00:03:12,919 --> 00:03:14,659
So you could say how many groups do you have?

66
00:03:14,659 --> 00:03:16,859
Well, you have four objects and each of

67
00:03:16,860 --> 00:03:21,290
them became two groups.

68
00:03:21,289 --> 00:03:22,269
I'm looking for a different color.

69
00:03:22,270 --> 00:03:24,520
Each of them became two groups, and so

70
00:03:24,520 --> 00:03:26,840
you also have eight.

71
00:03:26,840 --> 00:03:30,710
So dividing by 1/2 is the same thing as multiplying by 2.

72
00:03:30,710 --> 00:03:32,250
And you could think about it with other numbers, but

73
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hopefully, that gives you a little bit of an intuition.

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