1
00:00:01,480 --> 00:00:05,791
Now we're going to look at
multiplying and dividing

2
00:00:05,791 --> 00:00:12,248
fractions. Let's start with
4 * 1/3.

3
00:00:13,010 --> 00:00:17,000
That means for lots of 1/3.

4
00:00:17,830 --> 00:00:24,444
So. There I
have for lots of 1/3.

5
00:00:25,460 --> 00:00:32,492
So I've got 1/3 + 1/3
+ 1/3 plus another third and

6
00:00:32,492 --> 00:00:36,008
I've got a total of 4

7
00:00:36,008 --> 00:00:41,177
thirds. Or if I put them as
a mixed fraction.

8
00:00:42,060 --> 00:00:45,188
That's one and 1/3.

9
00:00:45,870 --> 00:00:49,836
And that's exactly the same as

10
00:00:49,836 --> 00:00:53,800
that. Usual multiplication if we

11
00:00:53,800 --> 00:00:58,380
have. 4 * 5 for
example.

12
00:00:59,670 --> 00:01:06,660
That means I've got five at 5 at
five at 5, which gives me 20.

13
00:01:08,190 --> 00:01:10,577
Fractions work in exactly
the same way.

14
00:01:11,770 --> 00:01:17,720
So if I had
2 * 1/5.

15
00:01:17,720 --> 00:01:20,928
I'd have 1/5 +

16
00:01:20,928 --> 00:01:23,918
1/5. Giving me to 5th.

17
00:01:25,700 --> 00:01:31,052
Now multiplication is
commutative. I just write that

18
00:01:31,052 --> 00:01:33,059
word down commutative.

19
00:01:35,940 --> 00:01:37,680
Now that means in now.

20
00:01:38,200 --> 00:01:41,775
Normal multiplication that 4 *

21
00:01:41,775 --> 00:01:47,384
5. Is exactly the same
as 5 * 4.

22
00:01:48,050 --> 00:01:55,550
Are 4 * 5 was 5
+ 5 + 5 + 5.

23
00:01:56,130 --> 00:02:03,890
And our 5 * 4 or 5 lots
of four is 4 + 4 + 4

24
00:02:03,890 --> 00:02:10,680
+ 4 + 4, so we have 4
five times and they are exactly

25
00:02:10,680 --> 00:02:13,105
the same, giving us 20.

26
00:02:14,070 --> 00:02:19,602
So it doesn't matter
whether I write 4 * 5 or 5

27
00:02:19,602 --> 00:02:22,368
* 4 because multiplication
is commutative.

28
00:02:23,830 --> 00:02:27,229
Well, let's see what that means
when we're looking at fractions.

29
00:02:27,980 --> 00:02:31,800
Let's say I have six

30
00:02:31,800 --> 00:02:35,770
times third. Multiplication is

31
00:02:35,770 --> 00:02:42,460
commutative. So that says it
should be the same as 1/3 * 6.

32
00:02:43,260 --> 00:02:50,460
Let's have a look
what that means. Six

33
00:02:50,460 --> 00:02:54,060
times the third 123456.

34
00:02:54,780 --> 00:03:02,556
So there's a third
plus 1/3 third, 3rd,

35
00:03:02,556 --> 00:03:05,472
third, plus 1/3.

36
00:03:06,060 --> 00:03:12,378
On this side, I've got
a third of six.

37
00:03:13,170 --> 00:03:16,341
So let's take

38
00:03:16,341 --> 00:03:17,398
612.

39
00:03:18,160 --> 00:03:22,110
34 56

40
00:03:23,360 --> 00:03:29,072
And I want a third of that six,
so it's like sharing it out

41
00:03:29,072 --> 00:03:30,296
between three people.

42
00:03:31,320 --> 00:03:33,725
There's one person's another and

43
00:03:33,725 --> 00:03:37,290
another. I want 1/3 so I'll just

44
00:03:37,290 --> 00:03:41,110
remove. The other 2/3.

45
00:03:41,110 --> 00:03:43,230
So my third of six.

46
00:03:43,860 --> 00:03:45,700
Is just like doing 6.

47
00:03:46,300 --> 00:03:48,868
Divided by three.

48
00:03:49,380 --> 00:03:51,004
And that gives us an answer of

49
00:03:51,004 --> 00:03:58,298
2. Well, what's my 1/3
add 1 third at 1/3?

50
00:03:58,940 --> 00:04:01,370
And, uh, the others together.

51
00:04:01,930 --> 00:04:09,850
And there I have two, so
here 12345 I get 6 thirds

52
00:04:09,850 --> 00:04:12,490
which gives Me 2.

53
00:04:13,020 --> 00:04:15,545
So I've shown that with

54
00:04:15,545 --> 00:04:19,438
fractions. It's exactly the
same, it's commutative.

55
00:04:20,010 --> 00:04:24,282
And that's what it looks like.
But with fractions you can see

56
00:04:24,282 --> 00:04:26,418
it in the two different ways.

57
00:04:26,960 --> 00:04:29,399
Either a fraction.

58
00:04:29,920 --> 00:04:31,288
Of a whole number.

59
00:04:31,800 --> 00:04:33,200
Like we had here.

60
00:04:34,610 --> 00:04:39,410
Or a fraction taking a
whole number of times like

61
00:04:39,410 --> 00:04:40,850
we had here.

62
00:04:42,730 --> 00:04:45,190
You guys out of the way.

63
00:04:46,700 --> 00:04:53,966
Let's look at
another example, 5

64
00:04:53,966 --> 00:04:57,350
lots. Of 2/3.

65
00:04:58,390 --> 00:05:05,830
So we've got
2/3 five times.

66
00:05:12,820 --> 00:05:20,338
So what we have here is 2
+ 2 + 2 + 2 +

67
00:05:20,338 --> 00:05:23,560
2 or actually 5 * 2.

68
00:05:24,170 --> 00:05:28,688
Thirds so we've
got 10 thirds.

69
00:05:29,740 --> 00:05:32,084
And 10 thirds if we write it as

70
00:05:32,084 --> 00:05:37,240
a mixed fraction. Is 3 whole
ones is 3 threes and nine and

71
00:05:37,240 --> 00:05:38,712
one third left over.

72
00:05:41,960 --> 00:05:44,732
Now any number can be
written as a fraction.

73
00:05:46,420 --> 00:05:49,780
For example, the number

74
00:05:49,780 --> 00:05:54,995
2. Can be written as
two over 1.

75
00:05:55,500 --> 00:05:58,269
For over 2.

76
00:05:58,880 --> 00:06:00,938
6 over 3.

77
00:06:01,520 --> 00:06:05,405
And so on. So we can write a

78
00:06:05,405 --> 00:06:10,110
whole number. With a
denominator, so it's a numerator

79
00:06:10,110 --> 00:06:14,610
and denominator, and these are
all equivalent fractions to that

80
00:06:14,610 --> 00:06:15,960
two over 1.

81
00:06:17,030 --> 00:06:20,414
So another example, 2

82
00:06:20,414 --> 00:06:27,620
* 3/4. We can write
as two over one, so we've made

83
00:06:27,620 --> 00:06:29,048
our whole number.

84
00:06:29,600 --> 00:06:31,208
Into a fraction.

85
00:06:32,110 --> 00:06:35,220
Times 3/4.

86
00:06:37,960 --> 00:06:41,544
So what we have here is 2 *

87
00:06:41,544 --> 00:06:45,356
3. And 1 *

88
00:06:45,356 --> 00:06:53,057
4. So 2 threes giving A6
and once for four. And if we put

89
00:06:53,057 --> 00:06:59,284
this as a fraction in its lowest
form, then we divide both the

90
00:06:59,284 --> 00:07:05,032
numerator and the denominator by
two. So we get three over 2.

91
00:07:05,710 --> 00:07:10,435
Or as a mixed
fraction 1 1/2.

92
00:07:12,240 --> 00:07:19,359
Let's look at another
example. This time 7 *

93
00:07:19,359 --> 00:07:20,941
5 ninths.

94
00:07:22,160 --> 00:07:28,606
So let's turn our Seven into
an equivalent fraction with. One

95
00:07:28,606 --> 00:07:30,364
is the denominator.

96
00:07:31,030 --> 00:07:34,290
Multiplied by five nights.

97
00:07:35,630 --> 00:07:38,330
So we've got 7 * 5.

98
00:07:38,890 --> 00:07:42,150
Over 1 * 9.

99
00:07:42,690 --> 00:07:48,780
So we have
35 over 9.

100
00:07:48,870 --> 00:07:50,750
Or as a mixed number.

101
00:07:52,660 --> 00:07:57,968
That's three. And
eight ninths.

102
00:07:59,880 --> 00:08:05,916
Now let's have a look at an
example where we're finding a

103
00:08:05,916 --> 00:08:07,928
fraction multiplied by another

104
00:08:07,928 --> 00:08:14,706
fraction. So let's take
1/3 * 1/2.

105
00:08:16,430 --> 00:08:20,500
And this means we want to take
1/3 of 1/2.

106
00:08:22,060 --> 00:08:23,368
So there's a half.

107
00:08:24,170 --> 00:08:31,046
And we want to split it
up into 3 equal pieces. Let's

108
00:08:31,046 --> 00:08:36,203
look numerically what we were
doing before multiplying the

109
00:08:36,203 --> 00:08:38,495
numerators and multiplying the

110
00:08:38,495 --> 00:08:46,014
denominators. So 1 * 1 is one
and 3 * 2 is 6, so we

111
00:08:46,014 --> 00:08:48,269
get an answer of 1/6.

112
00:08:49,080 --> 00:08:52,460
Well, let's have a look. If we
put some 6.

113
00:08:53,420 --> 00:08:55,170
On here we can see.

114
00:08:55,680 --> 00:08:59,285
36 is the same as a half.

115
00:09:00,300 --> 00:09:03,780
So if we split 1/2 into 3 equal

116
00:09:03,780 --> 00:09:09,190
sized pieces. And we want 1/3.
We want one of those pieces.

117
00:09:09,190 --> 00:09:11,045
Then we get one 6th.

118
00:09:12,710 --> 00:09:15,812
Let's look at

119
00:09:15,812 --> 00:09:22,116
another example.
Let's do 1/3

120
00:09:22,116 --> 00:09:24,360
* 2/5.

121
00:09:26,180 --> 00:09:32,102
So this time we want a
third of 2/5.

122
00:09:32,980 --> 00:09:34,708
So there's 2/5.

123
00:09:36,110 --> 00:09:38,084
And we want to split it into.

124
00:09:38,900 --> 00:09:41,688
Three equally sized pieces.

125
00:09:43,500 --> 00:09:47,300
Let's have a look again
numerically and then look to

126
00:09:47,300 --> 00:09:49,500
see. What we get visually.

127
00:09:50,430 --> 00:09:53,790
So 1 * 2 we multiply the

128
00:09:53,790 --> 00:10:01,280
numerators. 3 * 5 multiplied
the denominators once too is 2,

129
00:10:01,280 --> 00:10:08,375
three 5:15. So the answer is
2. Fifteenths. Well, how does

130
00:10:08,375 --> 00:10:10,310
that come about?

131
00:10:11,750 --> 00:10:18,390
Well. Instead of trying to
split those 2/5 into 3 pieces,

132
00:10:18,390 --> 00:10:23,956
is actually much easier to
imagine it as splitting 1/5 into

133
00:10:23,956 --> 00:10:30,171
3 pieces. The other fifth into
three pieces, and then taking

134
00:10:30,171 --> 00:10:32,047
one section from each.

135
00:10:33,800 --> 00:10:34,928
If we split.

136
00:10:35,580 --> 00:10:40,896
5th into three pieces instead of
five pieces, making it a whole

137
00:10:40,896 --> 00:10:45,562
1. Well, actually have 15
pieces making our whole one

138
00:10:45,562 --> 00:10:49,442
'cause they'll be 3 pieces
from each of the fifths.

139
00:10:50,580 --> 00:10:55,364
So that's where our 15th comes
from, and then we take one of

140
00:10:55,364 --> 00:10:59,412
the three pieces from this
fifth and one of the three

141
00:10:59,412 --> 00:11:03,092
pieces from this 5th, which
gets us are two fifteenths.

142
00:11:04,340 --> 00:11:08,480
Let's do a few more
examples.

143
00:11:09,920 --> 00:11:13,442
Let's say we have 2/5 *

144
00:11:13,442 --> 00:11:19,562
4 ninths. So what we're doing
each time it was when

145
00:11:19,562 --> 00:11:22,838
multiplying the numerators
together, and we're multiplying

146
00:11:22,838 --> 00:11:24,242
their denominators together.

147
00:11:25,010 --> 00:11:32,160
240859.
A 45 so we have

148
00:11:32,160 --> 00:11:33,640
840 fifths.

149
00:11:34,760 --> 00:11:40,478
And another one 2/3
* 4/5.

150
00:11:43,110 --> 00:11:46,080
So we've got 2 * 4.

151
00:11:46,660 --> 00:11:49,410
Divided by 3 * 5.

152
00:11:50,160 --> 00:11:56,970
2 falls right three 5:15
so we have eight fifteenths.

153
00:11:58,830 --> 00:12:04,077
Now, if we just think about
what we've been doing here,

154
00:12:04,077 --> 00:12:07,893
we've been taking a fraction
of another fraction.

155
00:12:09,100 --> 00:12:13,030
And because the fractions we've
been dealing with our proper

156
00:12:13,030 --> 00:12:17,746
fractions there less than one,
so 2/3 is less than one. We're

157
00:12:17,746 --> 00:12:22,462
taking 2/3 of four fifths. Then
we expect an answer that smaller

158
00:12:22,462 --> 00:12:26,785
because we're taking a fraction
of the four fifths, or a

159
00:12:26,785 --> 00:12:31,894
fraction of the four nights. So
in all these cases, we have an

160
00:12:31,894 --> 00:12:35,824
answer which is actually smaller
than the fraction we started

161
00:12:35,824 --> 00:12:40,147
with, which is what we expect is
we're taking a fraction.

162
00:12:40,210 --> 00:12:42,190
Smaller fraction of it.

163
00:12:43,100 --> 00:12:45,640
Let's do another example.

164
00:12:46,570 --> 00:12:52,499
This time let's have
2/3 * 9/10.

165
00:12:54,040 --> 00:13:00,110
So we have 2 * 9
/ 3 * 10.

166
00:13:01,470 --> 00:13:05,930
290 eighteen
three tens 30.

167
00:13:06,950 --> 00:13:12,900
Now we need to realize that this
is not a fraction in its lowest

168
00:13:12,900 --> 00:13:18,425
form, so we would need to find
the lowest form the both even

169
00:13:18,425 --> 00:13:23,100
numbers. So we can divide both
numerator and denominator by two

170
00:13:23,100 --> 00:13:24,800
and get 9 fifteenths.

171
00:13:25,740 --> 00:13:31,746
But let's just look back at this
stage. If I write it out again.

172
00:13:31,750 --> 00:13:34,798
And we could have avoided that.

173
00:13:35,320 --> 00:13:40,180
Because what we can do is some
counseling before we actually do

174
00:13:40,180 --> 00:13:45,367
the calculation. We can see
we've got a 9 here and the three

175
00:13:45,367 --> 00:13:49,411
here so we can divide both the
numerator and the denominator by

176
00:13:49,411 --> 00:13:54,370
three. When we divide the
numerator by three 3, three to

177
00:13:54,370 --> 00:13:58,627
nine goes three times. When we
divide the denominator by three,

178
00:13:58,627 --> 00:13:59,788
it goes once.

179
00:14:00,420 --> 00:14:04,424
And if we look further, we can
see that we can also divide by

180
00:14:04,424 --> 00:14:11,048
two. Two goes into two once and
two goes into 10 five times.

181
00:14:11,810 --> 00:14:19,118
So this is actually 1 * 3 / 1
* 5 and we get 3/5 and in fact

182
00:14:19,118 --> 00:14:23,178
you can see here that I didn't
look closely enough.

183
00:14:23,810 --> 00:14:28,990
And divide in fact by three.
It's easy to miss. So if you can

184
00:14:28,990 --> 00:14:33,060
make it easier for yourself and
do some counseling, then you

185
00:14:33,060 --> 00:14:36,020
should do so. So we end up with

186
00:14:36,020 --> 00:14:43,131
3/5. Let's look at
one more, this time

187
00:14:43,131 --> 00:14:48,369
involving three
fractions. So let's have

188
00:14:48,369 --> 00:14:50,988
1/2 * 3/4.

189
00:14:52,060 --> 00:14:54,658
Multiplied by 2/3.

190
00:14:55,360 --> 00:14:59,152
Exactly the same process as
before when multiplying

191
00:14:59,152 --> 00:15:03,418
fractions, so we multiply the
numerators doesn't matter how

192
00:15:03,418 --> 00:15:07,210
many there are, so it's 1 * 3

193
00:15:07,210 --> 00:15:14,586
* 2. And we multiply the
denominators so it's 2 * 4 * 3.

194
00:15:15,110 --> 00:15:18,830
Now before we go any further,
let's have a look if there's

195
00:15:18,830 --> 00:15:20,070
anything we can cancel.

196
00:15:20,660 --> 00:15:25,249
Well, yes, we've got two goes
into two. Once two goes into two

197
00:15:25,249 --> 00:15:28,670
once. We can divide by

198
00:15:28,670 --> 00:15:36,130
three. So we end up with 1
* 1 * 1. The top that's one and

199
00:15:36,130 --> 00:15:41,098
1 * 4 * 1. Just giving us an
answer of 1/4.

200
00:15:42,860 --> 00:15:48,138
OK, So what happens when we have
mixed fractions and we want to

201
00:15:48,138 --> 00:15:52,854
multiply them? Well, let's have
a look at some examples.

202
00:15:53,830 --> 00:15:59,366
We've got two and assert
multiplied by 3/4.

203
00:16:00,420 --> 00:16:05,659
Well, what we need to do is to
turn this mixed fraction into

204
00:16:05,659 --> 00:16:09,689
an improper fraction, because
when we've done that, we can

205
00:16:09,689 --> 00:16:13,719
simply do as well do what
we've already been doing,

206
00:16:13,719 --> 00:16:16,137
multiply the numerators
multiplied the denominators.

207
00:16:17,370 --> 00:16:22,844
So here we need to turn our two
whole ones into thirds, so it

208
00:16:22,844 --> 00:16:27,536
needs to go over three, so two
whole ones times by three.

209
00:16:28,200 --> 00:16:31,872
Then at this one here, and
that's how many thirds we have.

210
00:16:32,970 --> 00:16:35,529
Multiplied by 3/4.

211
00:16:37,020 --> 00:16:43,257
236 plus one so that
7 thirds times 3/4.

212
00:16:44,290 --> 00:16:50,637
Three goes into three, once in
2, three once, so having

213
00:16:50,637 --> 00:16:56,984
cancelled, we end up with Seven
quarters or one and 3/4.

214
00:16:57,830 --> 00:17:03,242
One
more

215
00:17:03,242 --> 00:17:08,610
example.
One and 2/5.

216
00:17:09,410 --> 00:17:13,550
Multiplied by
two and five 6.

217
00:17:15,710 --> 00:17:19,490
Again, mixed fractions need to
be turned into improper

218
00:17:19,490 --> 00:17:22,230
fractions. So here we have.

219
00:17:22,910 --> 00:17:26,834
1 * 5 'cause that
tells us how many.

220
00:17:28,110 --> 00:17:33,479
5th we have with our whole 1
five of them, plus the two

221
00:17:33,479 --> 00:17:37,609
that's our total number of
fifths multiplied by. We need

222
00:17:37,609 --> 00:17:43,391
the two whole ones in terms of
Sixths, so that's two lots of 6.

223
00:17:44,110 --> 00:17:45,898
Plus the five.

224
00:17:46,550 --> 00:17:49,268
And that's a number of 6th.

225
00:17:50,510 --> 00:17:57,422
Once five is 5 + 2
is 7 Seven fifths multiplied by

226
00:17:57,422 --> 00:18:04,334
two, 6 is a 12 plus
the five is 17 / 6.

227
00:18:05,510 --> 00:18:11,555
Quick check now. There's nothing
we can cancel their so 7 * 17.

228
00:18:12,090 --> 00:18:18,399
Seven 10s of $0.77 of
49. So it's 119.

229
00:18:18,560 --> 00:18:22,204
Six 5:30 so it's

230
00:18:22,204 --> 00:18:27,837
119th 30th. And we
had mixed fractions to start

231
00:18:27,837 --> 00:18:31,446
with, so let's turn this back
into mixed fractions.

232
00:18:32,030 --> 00:18:36,750
Well, three 30s are 90, so
that's three whole ones.

233
00:18:37,330 --> 00:18:41,840
And 20 nine 30th
leftover.

234
00:18:43,080 --> 00:18:47,336
So to multiply fractions,
you multiply the numerators

235
00:18:47,336 --> 00:18:51,060
together, and you multiply
the denominators together.

236
00:18:52,140 --> 00:18:55,847
If you start with a mixed
fraction, you need to turn

237
00:18:55,847 --> 00:18:59,217
it to an improper fraction
first before you do the

238
00:18:59,217 --> 00:18:59,554
multiplication.

239
00:19:00,720 --> 00:19:04,576
Let's go on to

240
00:19:04,576 --> 00:19:05,540
division.

241
00:19:06,100 --> 00:19:14,489
1/4
Divided by two.

242
00:19:15,460 --> 00:19:17,970
So we'll look at 1/4.

243
00:19:19,300 --> 00:19:21,940
We want to split it up into two

244
00:19:21,940 --> 00:19:25,208
pieces. So 2 equal pieces.

245
00:19:26,530 --> 00:19:29,038
Well, 2 equal pieces.

246
00:19:29,840 --> 00:19:33,368
That's two equal pieces
fitting on top.

247
00:19:36,350 --> 00:19:42,530
Each one is 1/8, so we split it
in half and we've got eights. If

248
00:19:42,530 --> 00:19:45,002
you can imagine our whole 1.

249
00:19:46,150 --> 00:19:48,280
And we had four quarters.

250
00:19:50,050 --> 00:19:55,570
If we have eighths, we have
eight pieces, each one is an

251
00:19:55,570 --> 00:19:59,710
eighth, so 2 eighths fit into
1/4, so 1/4.

252
00:20:00,230 --> 00:20:03,954
Divided into 2 bits
gives us 1/8.

253
00:20:07,700 --> 00:20:10,680
Now dividing by two.

254
00:20:11,490 --> 00:20:14,310
Is the same.

255
00:20:14,370 --> 00:20:17,100
Is multiplying.

256
00:20:18,590 --> 00:20:19,660
By half

257
00:20:22,730 --> 00:20:27,160
So quarter Divided by
two.

258
00:20:28,340 --> 00:20:31,958
Is equal to the same as

259
00:20:31,958 --> 00:20:37,010
a quarter? Multiplied
by half.

260
00:20:38,490 --> 00:20:40,365
I went back to multiplying

261
00:20:40,365 --> 00:20:46,210
fractions. What's 1 *
1 at the top and 4 *

262
00:20:46,210 --> 00:20:48,625
2 giving us our 8th?

263
00:20:49,840 --> 00:20:54,823
So this statement here is
exactly the same as this one

264
00:20:54,823 --> 00:20:57,088
here, because dividing by two.

265
00:20:57,700 --> 00:21:00,150
Is the same as
multiplying by half.

266
00:21:02,180 --> 00:21:07,207
Let's have a look at another
example, a third this time.

267
00:21:07,900 --> 00:21:10,648
Divided by 4.

268
00:21:12,450 --> 00:21:15,138
So we want to split our third.

269
00:21:15,950 --> 00:21:17,660
Into four pieces.

270
00:21:20,100 --> 00:21:22,520
Well, dividing by 4.

271
00:21:23,550 --> 00:21:26,628
This is the same as multiplying

272
00:21:26,628 --> 00:21:33,690
by quarter. So what we have
is 1 * 1 for

273
00:21:33,690 --> 00:21:40,509
the numerator. And 3 *
4 which is 12 for the

274
00:21:40,509 --> 00:21:44,677
denominator. So we're third
split into four pieces.

275
00:21:45,300 --> 00:21:46,740
Gives us a 12th.

276
00:21:47,780 --> 00:21:49,440
Again, if you sync.

277
00:21:50,670 --> 00:21:54,430
Of each of these thirds being
split into four pieces.

278
00:21:55,080 --> 00:21:59,373
We've got for their for
their, for their, so

279
00:21:59,373 --> 00:22:01,758
our whole is 12 pieces.

280
00:22:04,220 --> 00:22:06,470
And we've taken one of them
because we wanted.

281
00:22:07,990 --> 00:22:13,870
1/3 / 1/4 divided into 4 bits.
So we take one of them, so we've

282
00:22:13,870 --> 00:22:15,046
got a 12th.

283
00:22:20,420 --> 00:22:28,020
Let's do 1/2 / 2
back to an easier one

284
00:22:28,020 --> 00:22:34,436
to see. There's a half split it
into and we all know what we

285
00:22:34,436 --> 00:22:37,660
get. Well, let's do it.

286
00:22:38,400 --> 00:22:42,998
Are divided by two is the same
as multiplying by 1/2?

287
00:22:43,670 --> 00:22:49,410
1/2 * 1/2 one times one is 122
to four 1/4, which exactly what

288
00:22:49,410 --> 00:22:53,920
we expected. Cut 1/2 in two and
you get a quarter.

289
00:22:54,850 --> 00:22:59,803
Now as we can write any whole
number as a fraction, I could

290
00:22:59,803 --> 00:23:01,708
write this as a half.

291
00:23:02,210 --> 00:23:05,350
Divided by two over 1.

292
00:23:06,250 --> 00:23:11,164
And then what's happening
here is what I'm doing

293
00:23:11,164 --> 00:23:16,078
when I multiply is. I'm
turning this upside down.

294
00:23:17,340 --> 00:23:24,594
So to divide fractions, what you
do is you take the divisor, the

295
00:23:24,594 --> 00:23:27,384
one that's doing the Dividing.

296
00:23:28,090 --> 00:23:30,148
And you turn it upside down.

297
00:23:30,740 --> 00:23:31,850
And you multiply.

298
00:23:32,480 --> 00:23:36,170
Let's do some

299
00:23:36,170 --> 00:23:42,830
more examples. Let's
do 1/2 divided

300
00:23:42,830 --> 00:23:44,930
by quarter.

301
00:23:48,520 --> 00:23:49,888
So we have 1/2.

302
00:23:50,500 --> 00:23:52,688
We take the divisor.

303
00:23:53,290 --> 00:23:57,690
We turn it upside down and
instead of dividing, we

304
00:23:57,690 --> 00:24:04,255
multiply. So what we have here
is 1 * 4 over 2 * 1, which is

305
00:24:04,255 --> 00:24:06,810
2. So we end up with two.

306
00:24:07,630 --> 00:24:12,050
So 1/2 /, 1/4? Well, let's just
look at that.

307
00:24:12,580 --> 00:24:18,924
That's a half, and that's saying
how many times does 1/4 fit into

308
00:24:18,924 --> 00:24:25,720
a half? Well, we know that
I've quarter fits into our half

309
00:24:25,720 --> 00:24:28,974
two times. And that's the answer

310
00:24:28,974 --> 00:24:36,300
we had. 3rd divided
by a fifth

311
00:24:36,300 --> 00:24:42,881
this time. So we've
got a third and we take the

312
00:24:42,881 --> 00:24:46,562
divisor. We turn it upside down
and we multiply.

313
00:24:47,490 --> 00:24:54,540
So we end up with
five thirds, or one and

314
00:24:54,540 --> 00:24:58,752
2/3. So what we're saying is,
we've got a third.

315
00:25:00,350 --> 00:25:01,910
How many fifths?

316
00:25:02,610 --> 00:25:04,478
Fit into a third.

317
00:25:07,200 --> 00:25:10,548
Well, those are 5th.

318
00:25:11,230 --> 00:25:15,780
Well, we can see that it goes
one whole one and part leftover.

319
00:25:15,780 --> 00:25:19,280
It doesn't go as much as twice.
It's part leftover.

320
00:25:19,910 --> 00:25:24,240
So there's our answer
one and 2/3, so it goes

321
00:25:24,240 --> 00:25:26,405
the whole time and 2/3.

322
00:25:27,760 --> 00:25:35,260
Let's look at a whole number
now divided by a fraction. So

323
00:25:35,260 --> 00:25:39,010
let's look at 2 / 1/8.

324
00:25:39,770 --> 00:25:41,750
So we're saying we've got two

325
00:25:41,750 --> 00:25:46,731
whole ones. And we want to know
how many eighths fit into the

326
00:25:46,731 --> 00:25:50,823
two whole ones. Well, if we
think about it, we know that

327
00:25:50,823 --> 00:25:53,551
there are 8 eights in a whole 1.

328
00:25:54,470 --> 00:26:00,224
So if we've got two whole ones,
there must be 16 eighths, so we

329
00:26:00,224 --> 00:26:02,279
know our answer is 16.

330
00:26:03,600 --> 00:26:07,740
Well, let's see what that looks
like if we use our rule.

331
00:26:09,030 --> 00:26:11,250
So we take out two.

332
00:26:12,880 --> 00:26:17,148
The divisor is our 8th,
so we turn it upside down

333
00:26:17,148 --> 00:26:21,416
and we multiply. And yet
we've got 2, eight, 416 /

334
00:26:21,416 --> 00:26:23,744
1 and we get our 16.

335
00:26:25,330 --> 00:26:28,360
Let's do 4.

336
00:26:29,140 --> 00:26:31,000
Divided by 1/3.

337
00:26:35,070 --> 00:26:40,389
So how many thirds fit into
four whole ones?

338
00:26:41,460 --> 00:26:45,588
We know that there are three
thirds in each hole. One, and

339
00:26:45,588 --> 00:26:47,308
we've got four of them.

340
00:26:48,230 --> 00:26:50,582
So we're going to end up with an

341
00:26:50,582 --> 00:26:56,430
answer of 12. But again, let's
look at that using our method.

342
00:26:56,430 --> 00:26:59,130
Here we multiply an we turn.

343
00:26:59,740 --> 00:27:03,907
The divisor upside down. So yes,
we get 12.

344
00:27:04,730 --> 00:27:09,149
Now so far without division,
we've only looked at.

345
00:27:10,210 --> 00:27:12,450
Fractions with
numerators of one.

346
00:27:14,040 --> 00:27:16,398
Let's now look at some others.

347
00:27:17,280 --> 00:27:21,200
Let's say we've got

348
00:27:21,200 --> 00:27:24,088
3/4. Divided by two.

349
00:27:25,250 --> 00:27:29,288
Same message
3/4.

350
00:27:30,950 --> 00:27:38,165
We can write the whole 1 as a
fraction so it's two over one to

351
00:27:38,165 --> 00:27:42,975
divide which in the divisor
upside down and we multiply.

352
00:27:42,980 --> 00:27:49,892
So we have 3 * 1 three over 2
floors are eight, so we have an

353
00:27:49,892 --> 00:27:55,508
answer of 3/8 and if we think
about it, if you visualize 3/4

354
00:27:55,508 --> 00:27:57,668
and splitting it in half.

355
00:27:58,230 --> 00:28:00,680
Quarter, split in half eighths.

356
00:28:01,470 --> 00:28:05,488
3/4 split in half will
be 3/8.

357
00:28:06,930 --> 00:28:10,158
3/5 this time.

358
00:28:11,910 --> 00:28:15,120
Divided by 4.

359
00:28:16,080 --> 00:28:22,920
So we're taking 3/5 splitting
up into four pieces. What

360
00:28:22,920 --> 00:28:26,340
do we end up with?

361
00:28:26,640 --> 00:28:33,860
3/5 We going to
divide by. Let's put it as a

362
00:28:33,860 --> 00:28:35,852
fraction 4 over 1.

363
00:28:35,890 --> 00:28:42,830
Turn the divisor upside down
and multiply so we have

364
00:28:42,830 --> 00:28:49,770
3 * 1 is 3
over 4 fives a twentieths.

365
00:28:49,770 --> 00:28:53,282
One more

366
00:28:53,282 --> 00:28:56,810
example. 2/3

367
00:28:58,030 --> 00:29:01,580
Divided by. 3/4

368
00:29:04,180 --> 00:29:06,200
What we're looking at here?

369
00:29:07,430 --> 00:29:09,029
Those are 2/3.

370
00:29:10,370 --> 00:29:14,096
We want to know there's 3/4.

371
00:29:15,140 --> 00:29:18,848
How many times 3/4?

372
00:29:19,540 --> 00:29:21,439
Fits into 2/3.

373
00:29:22,020 --> 00:29:25,400
Well, you can see it doesn't go
a whole 1.

374
00:29:26,050 --> 00:29:30,307
So we can expect our answer to
be less than one.

375
00:29:30,960 --> 00:29:36,922
Because 3/4 is actually bigger
than 2/3. Well, let's have a

376
00:29:36,922 --> 00:29:43,436
look. 2/3 turn the
divisor upside down and

377
00:29:43,436 --> 00:29:49,584
multiply. So we have two falls
at 8 and 3 threes and nine so we

378
00:29:49,584 --> 00:29:54,218
get 8 ninths, 9 nights or whole
one. So it's just under a whole

379
00:29:54,218 --> 00:29:58,852
one which is what we can see
when we look at it visually. How

380
00:29:58,852 --> 00:30:00,838
many times this fits into this?

381
00:30:01,610 --> 00:30:08,270
Finally, how do we deal
with mixed fractions? Well,

382
00:30:08,270 --> 00:30:15,670
let's have a look at
an example. We've got one

383
00:30:15,670 --> 00:30:19,370
and 2/3 /, 2 1/4.

384
00:30:19,460 --> 00:30:25,674
And it's exactly the same as we
did before. We must turn mixed

385
00:30:25,674 --> 00:30:29,498
fractions into improper
fractions before we do the

386
00:30:29,498 --> 00:30:31,888
division. So one and 2/3.

387
00:30:32,470 --> 00:30:39,197
Is one lot of
3 + 2/3.

388
00:30:39,200 --> 00:30:44,696
Divided by two and a quarter
turn the two whole ones into

389
00:30:44,696 --> 00:30:50,192
quarters. That's 2 * 4. Add the
1/4. That's how many quarters

390
00:30:50,192 --> 00:30:57,566
we've got. Once three is
3 + 2, is 5 thirds

391
00:30:57,566 --> 00:31:01,370
divided by 248 Plus One is

392
00:31:01,370 --> 00:31:08,753
nine quarters. To divide, we
turn the divisor upside down and

393
00:31:08,753 --> 00:31:14,036
we multiply so that becomes
multiplied by 4. Ninths.

394
00:31:14,820 --> 00:31:17,277
Can we do any counseling now? We

395
00:31:17,277 --> 00:31:20,200
can't. Four 520

396
00:31:20,700 --> 00:31:26,244
Three 927 Seven answer of
2020 sevenths.

397
00:31:27,620 --> 00:31:33,276
And another
example, 2

398
00:31:33,276 --> 00:31:38,932
4/5 /
4 and

399
00:31:38,932 --> 00:31:44,337
2/3. We need to
turn these into improper

400
00:31:44,337 --> 00:31:49,869
fractions, so we've got two lots
of five. That's the whole ones

401
00:31:49,869 --> 00:31:54,479
turned into fifths. Plus the
four. That's how many fifths

402
00:31:54,479 --> 00:32:00,011
we've got divided by four whole
ones. We need them turned into

403
00:32:00,011 --> 00:32:02,316
thirds. That's 4 * 3.

404
00:32:03,080 --> 00:32:06,335
Plus the two, that's how
many thirds.

405
00:32:07,750 --> 00:32:14,490
2 fives are 10 +
4 is 14 fifths divided

406
00:32:14,490 --> 00:32:20,556
by 3/4 of 12 +
2 is 14 thirds.

407
00:32:21,100 --> 00:32:27,196
To divide fractions, you
turn the divisor upside

408
00:32:27,196 --> 00:32:30,244
down and you multiply.

409
00:32:31,280 --> 00:32:35,965
Check for. Anything that's
common to both so we can divide

410
00:32:35,965 --> 00:32:38,170
through here by 14. That saves a

411
00:32:38,170 --> 00:32:43,046
lot of calculation. And we
end up with once three is 3

412
00:32:43,046 --> 00:32:46,786
at the top five 15. So an
answer of 3/5.