1
00:00:00,000 --> 00:00:00,810


2
00:00:00,810 --> 00:00:03,609
We're now going to learn how to go from mixed numbers to

3
00:00:03,609 --> 00:00:05,679
improper fractions and vice versa.

4
00:00:05,679 --> 00:00:07,119
So first a little bit of terminology.

5
00:00:07,120 --> 00:00:08,490
What is a mixed number?

6
00:00:08,490 --> 00:00:10,349
Well, you've probably seen someone write, let's

7
00:00:10,349 --> 00:00:13,849
say, 2 and 1/2.

8
00:00:13,849 --> 00:00:15,469
This is a mixed number.

9
00:00:15,470 --> 00:00:16,949
You're saying why is it a mixed number?

10
00:00:16,949 --> 00:00:21,519
Well, because we're including a whole number and a fraction.

11
00:00:21,519 --> 00:00:22,629
So that's why it's a mixed number.

12
00:00:22,629 --> 00:00:24,509
It's a whole number mixed with a fraction.

13
00:00:24,510 --> 00:00:25,240
So 2 and 1/2.

14
00:00:25,239 --> 00:00:27,759
And I think you have a sense of what 2 and 1/2 is.

15
00:00:27,760 --> 00:00:31,050
It's some place halfway between 2 and 3.

16
00:00:31,050 --> 00:00:32,085
And what's an improper fractional?

17
00:00:32,085 --> 00:00:36,259
Well an Improper fraction is a fraction where the numerator is

18
00:00:36,259 --> 00:00:37,409
larger than the denominator.

19
00:00:37,409 --> 00:00:39,329
So let's give an example of an improper fraction.

20
00:00:39,329 --> 00:00:41,140
I'm just going to pick some random numbers.

21
00:00:41,140 --> 00:00:47,759
Let's say I had 23 over 5.

22
00:00:47,759 --> 00:00:49,390
This is an improper fraction.

23
00:00:49,390 --> 00:00:50,090
Why?

24
00:00:50,090 --> 00:00:52,290
Because 23 is larger than 5.

25
00:00:52,289 --> 00:00:54,030
It's that simple.

26
00:00:54,030 --> 00:00:57,450
It turns out that you can convert an improper fraction

27
00:00:57,450 --> 00:01:00,040
into a mixed number or a mixed number into an

28
00:01:00,039 --> 00:01:01,359
improper fraction.

29
00:01:01,359 --> 00:01:02,789
So let's start with the latter.

30
00:01:02,789 --> 00:01:05,379
Let's learn how to do a mixed number into an

31
00:01:05,379 --> 00:01:06,599
improper fraction.

32
00:01:06,599 --> 00:01:10,019
So first I'll just show you kind of just the basic

33
00:01:10,019 --> 00:01:11,390
systematic way of doing it.

34
00:01:11,390 --> 00:01:13,189
It'll always give you the right answer, and then hopefully I'll

35
00:01:13,189 --> 00:01:15,109
give you a little intuition for why it works.

36
00:01:15,109 --> 00:01:18,875
So if I wanted to convert 2 and 1/2 into an improper fraction

37
00:01:18,875 --> 00:01:22,900
or I want to unmix it you could say, all I do is I take the

38
00:01:22,900 --> 00:01:27,190
denominator in the fraction part, multiply it by the whole

39
00:01:27,189 --> 00:01:30,149
number, and add the numerator.

40
00:01:30,150 --> 00:01:31,130
So let's do that.

41
00:01:31,129 --> 00:01:33,579
I think if we do enough examples you'll

42
00:01:33,579 --> 00:01:34,599
get the pattern.

43
00:01:34,599 --> 00:01:40,339
So 2 times 2 is 4 plus 1 is 5.

44
00:01:40,340 --> 00:01:41,040
So let's write that.

45
00:01:41,040 --> 00:01:46,330
It's 2 times 2 plus 1, and that's going to

46
00:01:46,329 --> 00:01:47,599
be the new numerator.

47
00:01:47,599 --> 00:01:50,319
And it's going to be all of that over the old denominator.

48
00:01:50,319 --> 00:01:52,542
So that equals 5/2.

49
00:01:52,543 --> 00:01:55,180


50
00:01:55,180 --> 00:01:58,410
So 2 and 1/2 is equal to 5/2.

51
00:01:58,409 --> 00:02:01,149


52
00:02:01,150 --> 00:02:02,260
Let's do another one.

53
00:02:02,260 --> 00:02:08,050
Let's say I had 4 and 2/3.

54
00:02:08,050 --> 00:02:11,950
This is equal to -- so this is going to be all over 3.

55
00:02:11,949 --> 00:02:13,489
We keep the denominator the same.

56
00:02:13,490 --> 00:02:18,180
And then new numerator is going to be 3 times 4 plus 2.

57
00:02:18,180 --> 00:02:24,040
So it's going to be 3 times 4, and then you're going to add 2.

58
00:02:24,039 --> 00:02:26,639
Well that equals 3 times 4 -- order of operations, you always

59
00:02:26,639 --> 00:02:28,729
do multiplication first, and that's actually the way

60
00:02:28,729 --> 00:02:30,939
I taught it how to convert this anyway.

61
00:02:30,939 --> 00:02:34,240
3 times 4 is 12 plus 2 is 14.

62
00:02:34,240 --> 00:02:38,340
So that equals 14 over 3.

63
00:02:38,340 --> 00:02:39,030
Let's do another one.

64
00:02:39,030 --> 00:02:48,710
Let's say I had 6 and 17/18.

65
00:02:48,710 --> 00:02:50,520
I gave myself a hard problem.

66
00:02:50,520 --> 00:02:54,450
Well, we just keep the denominator the same.

67
00:02:54,449 --> 00:02:57,191
And then new numerator is going to be 18 times 6

68
00:02:57,192 --> 00:03:03,960
or 6 times 18 plus 17.

69
00:03:03,960 --> 00:03:05,200
Well 6 times 18.

70
00:03:05,199 --> 00:03:08,009
Let's see, that's 60 plus 48 it's 108, so that

71
00:03:08,009 --> 00:03:11,909
equals 108 plus 17.

72
00:03:11,909 --> 00:03:14,310
All that over 18.

73
00:03:14,310 --> 00:03:20,069
108 plus 17 is equal to 125 over 18.

74
00:03:20,069 --> 00:03:29,150
So, 6 and 17/18 is equal to 125 over 18.

75
00:03:29,150 --> 00:03:30,099
Let's do a couple more.

76
00:03:30,099 --> 00:03:32,810
And in a couple minutes I'm going to teach you how to go

77
00:03:32,810 --> 00:03:35,699
the other way, how to go from an improper fraction

78
00:03:35,699 --> 00:03:36,639
to a mixed number.

79
00:03:36,639 --> 00:03:39,879


80
00:03:39,879 --> 00:03:41,680
And this one I'm going to try to give you a little bit of

81
00:03:41,680 --> 00:03:44,849
intuition for, why what I'm teaching you actually works.

82
00:03:44,849 --> 00:03:48,049
So let's say 2 and 1/4.

83
00:03:48,050 --> 00:03:51,930


84
00:03:51,930 --> 00:03:54,920
If we use the -- I guess you'd call it a system that I just

85
00:03:54,919 --> 00:04:04,139
showed you -- that equals 4 times 2 plus 1 over 4.

86
00:04:04,139 --> 00:04:09,719
Well that equals, 4 times 2 is 8 plus 1 is 9, 9 over 4.

87
00:04:09,719 --> 00:04:14,109
I want to give you an intuition for why this actually works.

88
00:04:14,110 --> 00:04:17,150
So 2 and 1/4, let's actually draw that, see what

89
00:04:17,149 --> 00:04:18,279
it looks like.

90
00:04:18,279 --> 00:04:22,199
So let's put this back into kind of the pie analogy.

91
00:04:22,199 --> 00:04:26,129
So that's equal to one pie.

92
00:04:26,129 --> 00:04:28,040
Two pies.

93
00:04:28,040 --> 00:04:33,840
And then let's say a 1/4 of a pie.

94
00:04:33,839 --> 00:04:34,899
A 1/4 is like this.

95
00:04:34,899 --> 00:04:38,349


96
00:04:38,350 --> 00:04:41,560
2 and 1/4, and ignore this, this is nothing.

97
00:04:41,560 --> 00:04:43,430
It's not a decimal point -- actually, let me erase it so it

98
00:04:43,430 --> 00:04:45,300
doesn't confuse you even more.

99
00:04:45,300 --> 00:04:51,900


100
00:04:51,899 --> 00:04:53,929
So go back to the pieces of the pie.

101
00:04:53,930 --> 00:04:58,490
So there's 2 and 1/4 pieces of pie.

102
00:04:58,490 --> 00:05:03,000
And we want to re-write this as just how many 1/4s

103
00:05:03,000 --> 00:05:04,800
of pie are there total.

104
00:05:04,800 --> 00:05:08,770
Well if we take each of these pieces -- I need to change the

105
00:05:08,769 --> 00:05:13,224
color -- if we take each of these pieces and we divide it

106
00:05:13,225 --> 00:05:17,800
into 1/4s, we can now say how many total 1/4s of

107
00:05:17,800 --> 00:05:19,060
pie do we have?

108
00:05:19,060 --> 00:05:28,490
Well we have 1, 2, 3, 4, 5, 6, 7, 8, 9 fourths.

109
00:05:28,490 --> 00:05:29,759
Makes sense, right?

110
00:05:29,759 --> 00:05:33,620
2 and 1/4 is the same thing as 9/4.

111
00:05:33,620 --> 00:05:36,920
And this will work with any fraction.

112
00:05:36,920 --> 00:05:37,830
So let's go the other way.

113
00:05:37,829 --> 00:05:41,699
Let's figure out how to go from an improper fraction

114
00:05:41,699 --> 00:05:43,680
to a mixed number.

115
00:05:43,680 --> 00:05:49,259
Let's say I had 23 over 5.

116
00:05:49,259 --> 00:05:51,079
So here we go in the opposite direction.

117
00:05:51,079 --> 00:05:53,289
We actually take the denominator, we say how

118
00:05:53,290 --> 00:05:55,080
many times does it go into the numerator.

119
00:05:55,079 --> 00:05:57,649
And then we figure out the remainder.

120
00:05:57,649 --> 00:06:03,219
So let's say 5 goes into 23 -- well, 5 goes

121
00:06:03,220 --> 00:06:05,400
into 23 four times.

122
00:06:05,399 --> 00:06:08,889
4 times 5 is 20.

123
00:06:08,889 --> 00:06:11,240
And the remainder is 3.

124
00:06:11,240 --> 00:06:17,150
So 23 over 5, we can say that's equal to 4 and in

125
00:06:17,149 --> 00:06:19,969
the remainder 3 over 5.

126
00:06:19,970 --> 00:06:22,860
So it's 4 and 3/5.

127
00:06:22,860 --> 00:06:25,449


128
00:06:25,449 --> 00:06:26,849
Let's review what we just did.

129
00:06:26,850 --> 00:06:29,220
We just took the denominator and divided it into

130
00:06:29,220 --> 00:06:30,140
the numerator.

131
00:06:30,139 --> 00:06:33,829
So 5 goes into 23 four times.

132
00:06:33,829 --> 00:06:38,050
And what's left over is 3.

133
00:06:38,050 --> 00:06:41,930
So, 5 goes into 23, 4 and 3/5 times.

134
00:06:41,930 --> 00:06:46,240
Or another way of saying that is 23 over 5 is 4 and 3/5.

135
00:06:46,240 --> 00:06:48,269
Let's do another example like that.

136
00:06:48,269 --> 00:06:51,849
Let's say 17 over 8.

137
00:06:51,850 --> 00:06:53,680
What does that equal as a mixed number?

138
00:06:53,680 --> 00:06:56,600
You can actually do this in your head, but I'll

139
00:06:56,600 --> 00:06:59,430
write it out just so you don't get confused.

140
00:06:59,430 --> 00:07:04,540
8 goes into 17 two times.

141
00:07:04,540 --> 00:07:07,550
2 times 8 is 16.

142
00:07:07,550 --> 00:07:09,379
17 minus 16 is 1.

143
00:07:09,379 --> 00:07:10,810
Remainder 1.

144
00:07:10,810 --> 00:07:19,060
So, 17 over 8 is equal to 2 -- that's this 2 -- and 1/8.

145
00:07:19,060 --> 00:07:22,610
Because we have one 8 left over.

146
00:07:22,610 --> 00:07:25,199
Let me show you kind of a visual way of representing this

147
00:07:25,199 --> 00:07:28,589
too, so it actually makes sense how this conversion is working.

148
00:07:28,589 --> 00:07:33,539
Let's say I had 5/2, right?

149
00:07:33,540 --> 00:07:37,780
So that literally means I have 5 halves, or if we go back to

150
00:07:37,779 --> 00:07:42,309
the pizza or the pie analogy, let's draw my five

151
00:07:42,310 --> 00:07:44,290
halves of pizza.

152
00:07:44,290 --> 00:07:49,879
So let's say I have one half of pizza here, and let's say I

153
00:07:49,879 --> 00:07:51,740
have another half of pizza here.

154
00:07:51,740 --> 00:07:54,530
I just flipped it over.

155
00:07:54,529 --> 00:07:55,339
So that's 2.

156
00:07:55,339 --> 00:07:57,719
So it's 1 half, 2 halves.

157
00:07:57,720 --> 00:08:00,860


158
00:08:00,860 --> 00:08:03,569
So that's three halves.

159
00:08:03,569 --> 00:08:05,379
And then I have a fourth half here.

160
00:08:05,379 --> 00:08:07,899
These are halves of pizza, and then I have a fifth

161
00:08:07,899 --> 00:08:10,659
half here, right?

162
00:08:10,660 --> 00:08:12,910
So that's 5/2.

163
00:08:12,910 --> 00:08:17,150
Well, if we look at this, if we combine these two halves, this

164
00:08:17,149 --> 00:08:21,750
is equal to 1 piece, I have another piece, and then I

165
00:08:21,750 --> 00:08:23,910
have half of a piece, right?

166
00:08:23,910 --> 00:08:31,330
So that is equal to 2 and 1/2 pieces of pie.

167
00:08:31,329 --> 00:08:33,009
Hopefully that doesn't confuse you too much.

168
00:08:33,009 --> 00:08:37,289
And if we wanted to do this the systematic way, we could have

169
00:08:37,289 --> 00:08:43,579
said 2 goes into 5 -- well, 2 goes into 5 two times, and

170
00:08:43,580 --> 00:08:46,560
that 2 is right here.

171
00:08:46,559 --> 00:08:49,169
And then 2 times 2 is 4.

172
00:08:49,169 --> 00:08:51,870
5 minus 4 is 1, so the remainder is 1, and

173
00:08:51,870 --> 00:08:54,049
that's what we use here.

174
00:08:54,049 --> 00:08:56,709
And of course, we keep the denominator the same.

175
00:08:56,710 --> 00:08:59,090
So 5/2 equals 2 and 1/2.

176
00:08:59,090 --> 00:09:01,530
Hopefully that gives you a sense of how to go from one

177
00:09:01,529 --> 00:09:04,569
mixed number to an improper fraction, and vice versa,

178
00:09:04,570 --> 00:09:07,520
from an improper fraction to a mixed number.

179
00:09:07,519 --> 00:09:09,659
If you're still confused let me know and I might

180
00:09:09,659 --> 00:09:11,659
make some more modules.

181
00:09:11,659 --> 00:09:12,740
Have fun with the exercises.

182
00:09:12,740 --> 00:09:14,039