1
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2
00:00:00,660 --> 00:00:01,229
Divide.

3
00:00:01,229 --> 00:00:04,769
Simplify the answer and write as a mixed number.

4
00:00:04,769 --> 00:00:08,230
And we have 2 and 1/4 divided by 1 and 3/4.

5
00:00:08,230 --> 00:00:10,150
So the first thing we want to do since both of these are

6
00:00:10,150 --> 00:00:12,259
mixed numbers is to convert them both

7
00:00:12,259 --> 00:00:13,500
into improper fractions.

8
00:00:13,500 --> 00:00:15,740
So let's start with 2 and 1/4.

9
00:00:15,740 --> 00:00:18,850
So we're still going to have 4 in the denominator, but

10
00:00:18,850 --> 00:00:21,030
instead of 2 and 1/4, remember, 2 is the

11
00:00:21,030 --> 00:00:22,679
same thing as 8/4.

12
00:00:22,679 --> 00:00:25,339
So we have 8/4, and then we have another 1/4.

13
00:00:25,339 --> 00:00:27,230
That gives us 9/4.

14
00:00:27,230 --> 00:00:31,899
Or another way to come up with this 9, you take 4 times 2,

15
00:00:31,899 --> 00:00:33,989
which is 8, plus 1.

16
00:00:33,990 --> 00:00:35,370
That gives you 9.

17
00:00:35,369 --> 00:00:38,719
And then the 1 and 3/4, same process.

18
00:00:38,719 --> 00:00:41,879
You're going to have 4 in the denominator, and then the

19
00:00:41,880 --> 00:00:46,780
numerator is going to be 4 times 1, which is 4, plus 3,

20
00:00:46,780 --> 00:00:48,450
which is 7.

21
00:00:48,450 --> 00:00:50,990
So this is the exact same problem here.

22
00:00:50,990 --> 00:00:55,370
2 and 1/4 divided by 1 and 3/4 is the same thing as 9/4

23
00:00:55,369 --> 00:00:57,859
divided by 7/4.

24
00:00:57,859 --> 00:01:01,200
And we saw in several videos already that dividing by a

25
00:01:01,200 --> 00:01:05,000
fraction is the same thing as multiplying by its reciprocal.

26
00:01:05,000 --> 00:01:09,900
So this is equivalent to-- so these are all equivalent.

27
00:01:09,900 --> 00:01:15,960
This is equivalent to 9/4 times the reciprocal of this.

28
00:01:15,959 --> 00:01:18,832
We're changing the division operation to a multiplication,

29
00:01:18,832 --> 00:01:21,390
and we're taking the reciprocal of the 7/4.

30
00:01:21,390 --> 00:01:24,489
For the reciprocal of 7/4, you swap the numerator and

31
00:01:24,489 --> 00:01:26,099
denominator, or the top number and the bottom

32
00:01:26,099 --> 00:01:29,729
number, and you get 4/7.

33
00:01:29,730 --> 00:01:31,950
Now, we could just multiply these.

34
00:01:31,950 --> 00:01:35,380
We could just say this is 9 times 4, which would be 36,

35
00:01:35,379 --> 00:01:38,589
over 4 times 7, which is 28, and then try to put it in

36
00:01:38,590 --> 00:01:40,900
lowest terms, or we could do it right now because it would

37
00:01:40,900 --> 00:01:41,290
be simpler.

38
00:01:41,290 --> 00:01:42,820
We have a 4 in the numerator.

39
00:01:42,819 --> 00:01:44,559
We have a 4 in the denominator, that'll

40
00:01:44,560 --> 00:01:47,079
eventually be in the denominator, so let's divide

41
00:01:47,079 --> 00:01:49,280
our eventual numerators and our eventual

42
00:01:49,280 --> 00:01:50,960
denominators both by 4.

43
00:01:50,959 --> 00:01:54,039
So you divide this 4 by 4, you get 1.

44
00:01:54,040 --> 00:01:56,070
This 4 by 4, you get 1.

45
00:01:56,069 --> 00:01:59,989
So now when you multiply it, you get 9 times 1, which is 9,

46
00:01:59,989 --> 00:02:03,659
over 1 times 7, which is 7.

47
00:02:03,659 --> 00:02:05,679
So we have our answer, but right now,

48
00:02:05,680 --> 00:02:07,150
it's an improper fraction.

49
00:02:07,150 --> 00:02:10,159
They want us to write it as a mixed number.

50
00:02:10,159 --> 00:02:12,560
And to figure it out as a mixed number, we can do it in

51
00:02:12,560 --> 00:02:13,159
our heads now.

52
00:02:13,159 --> 00:02:15,159
I think we've seen this enough times.

53
00:02:15,159 --> 00:02:20,189
We say how many times does 7 go into 9?

54
00:02:20,189 --> 00:02:24,020
Well, it goes into it exactly one time, but when you take 7

55
00:02:24,020 --> 00:02:26,719
into 9 one time, what do you have left over?

56
00:02:26,719 --> 00:02:28,189
Well, you're going to have 2 left over, right?

57
00:02:28,189 --> 00:02:31,650
7 times 1 is 7, and you're going to have 2 left over.

58
00:02:31,650 --> 00:02:33,015
You need 2 more to get to 9.

59
00:02:33,014 --> 00:02:37,919
So you're going to have 2 left over, so this is 1 and 2/7.

60
00:02:37,919 --> 00:02:39,519
And we're done!

61
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