0:00:02.240,0:00:06.227
This tutorial is about the basic[br]concepts of fractions.
0:00:06.760,0:00:11.200
What they are, what they look[br]like, and why we have them.
0:00:12.340,0:00:17.048
A function is a way of writing[br]part of a whole.
0:00:17.770,0:00:22.814
And it's formed when we divide a[br]whole into an equal number of
0:00:22.814,0:00:27.370
pieces. Now let's have a look.[br]I've got a representation here.
0:00:28.120,0:00:29.080
Of a whole.
0:00:30.200,0:00:36.752
And let's say we want to divide[br]it into 4 equal pieces.
0:00:38.520,0:00:44.760
So there we've[br]taken 1 hole
0:00:44.760,0:00:51.000
and divided it[br]into 4 equal
0:00:51.000,0:00:57.240
pieces. So each[br]piece represents 1/4.
0:00:58.510,0:00:59.810
Wow.
0:01:00.870,0:01:04.180
I've now taken 1/4 away.
0:01:05.800,0:01:09.436
Now I've removed
0:01:09.436,0:01:15.060
two quarters. If[br]I take a third.
0:01:15.990,0:01:22.986
That's 3/4.[br]And if I take the false so I've
0:01:22.986,0:01:24.821
now got all four pieces.
0:01:25.440,0:01:30.401
I've taken all of them for[br]quarters, which is exactly the
0:01:30.401,0:01:32.656
same as taking the whole.
0:01:33.240,0:01:38.080
Let's just return for a moment[br]to the two quarters.
0:01:38.600,0:01:42.840
Now[br]two
0:01:42.840,0:01:46.494
quarters. Is exactly
0:01:46.494,0:01:52.695
the same. As if I'd started[br]with my whole and actually
0:01:52.695,0:01:54.210
divided it into.
0:01:55.010,0:01:57.610
2 pieces of equal size.
0:01:58.450,0:02:00.202
And you can see that that's
0:02:00.202,0:02:06.040
exactly the same. As two[br]quarters so I can write two
0:02:06.040,0:02:10.480
quarters. As one[br]half.
0:02:12.270,0:02:15.998
Let's have a look at[br]another illustration now.
0:02:17.190,0:02:19.395
Here I have a bar of chocolate.
0:02:20.740,0:02:22.369
It's been divided.
0:02:22.930,0:02:29.144
Into six pieces of equal size.[br]So we've taken a whole bar and
0:02:29.144,0:02:31.534
divide it into six pieces.
0:02:32.270,0:02:36.540
So each piece is[br]16.
0:02:38.330,0:02:42.506
Now, let's say I'm going to[br]share my bar of chocolate with
0:02:42.506,0:02:43.550
the camera man.
0:02:44.650,0:02:50.770
So I want to divide the bar[br]of chocolate into two pieces.
0:02:51.370,0:02:53.170
So if I do that.
0:02:55.160,0:02:59.060
Where each going to have one
0:02:59.060,0:03:05.940
236. So 1/2 is[br]exactly the same as 36.
0:03:06.810,0:03:11.139
But there's not just one[br]cameraman. We've got two
0:03:11.139,0:03:16.430
cameramen, so I need to share[br]it. Actually, between three of
0:03:16.430,0:03:23.475
us. So now if I put my bar back[br]together and I need to share it
0:03:23.475,0:03:27.060
between 3:00. Where[br]each going to get.
0:03:28.430,0:03:30.810
Two pieces.
0:03:32.550,0:03:38.110
So 1/3 is exactly the[br]same as 26.
0:03:38.910,0:03:45.540
But Let's say I[br]want to eat all my chocolate bar
0:03:45.540,0:03:51.169
myself, so I'm going to have all[br]six pieces, so they're all mine.
0:03:51.700,0:03:55.693
Not going to share them, so I[br]take all six pieces.
0:03:56.310,0:03:58.596
And I've taken away the whole
0:03:58.596,0:03:58.977
bar.
0:03:59.540,0:04:06.470
So.[br]Fractions we can look at.
0:04:07.010,0:04:08.348
In two ways.
0:04:09.320,0:04:13.200
We can look at it as the number
0:04:13.200,0:04:15.850
of pieces. That we've used.
0:04:17.130,0:04:23.610
Divided by the[br]number of pieces.
0:04:24.280,0:04:27.260
That make a whole.
0:04:27.260,0:04:32.950
Oh
0:04:33.990,0:04:36.888
As the whole.
0:04:37.710,0:04:44.173
Divided by. Number of pieces[br]or number of people that we've
0:04:44.173,0:04:45.484
divided it into.
0:04:46.290,0:04:52.494
So here we have a whole bar[br]divided into 6 pieces.
0:04:53.880,0:04:57.510
Here we have the number of[br]pieces that we've taken divided
0:04:57.510,0:05:01.470
note 5 the number of pieces that[br]make up the whole bar.
0:05:03.540,0:05:10.828
Let's have a look[br]at some other fractions.
0:05:10.830,0:05:16.926
Let's say[br]we have
0:05:16.926,0:05:18.450
3/8.
0:05:20.000,0:05:25.352
So we've divided a whole up into[br]8 pieces of equal size.
0:05:25.890,0:05:27.636
And we've taken three of them.
0:05:28.270,0:05:29.590
3/8
0:05:31.150,0:05:34.960
We could have 11 twelfths.
0:05:35.800,0:05:41.767
So we've divided a whole up into[br]12 pieces and taking eleven of
0:05:41.767,0:05:46.060
them. We could have[br]7/10.
0:05:47.160,0:05:52.424
Here we will have divided a hole[br]into 10 pieces of equal size and
0:05:52.424,0:05:53.928
taken Seven of them.
0:05:54.710,0:05:56.238
And we can have.
0:05:56.800,0:06:04.696
Any numbers in our fraction so[br]we could have 105 hundreds or
0:06:04.696,0:06:07.986
three 167th and so on.
0:06:08.900,0:06:12.165
Now we've looked at representing
0:06:12.165,0:06:16.897
fractions. Using piece of Cod[br]circular representation are
0:06:16.897,0:06:19.452
rectangle with our bar of
0:06:19.452,0:06:24.008
chocolate. Let's have a look at[br]one more before we move on and
0:06:24.008,0:06:25.478
let's let's see it on.
0:06:26.110,0:06:28.000
A section of number line.
0:06:29.560,0:06:31.877
So let's say we have zero here.
0:06:32.540,0:06:34.439
And one here.
0:06:34.950,0:06:37.302
So let's look at what 3/8 might
0:06:37.302,0:06:44.150
look like. While I need to[br]divide my section into 8 pieces
0:06:44.150,0:06:45.818
of equal size.
0:06:46.690,0:06:49.993
Now obviously this is an[br]illustration, so I'm not
0:06:49.993,0:06:53.663
actually getting my router[br]out to make sure I've got
0:06:53.663,0:06:54.764
equal size pieces.
0:06:55.830,0:07:01.894
But hopefully. That's about[br]right. So we've got 12345678
0:07:01.894,0:07:09.238
pieces of equal size and I'm[br]going to take three of them.
0:07:09.238,0:07:12.910
So if I take 1, two
0:07:12.910,0:07:17.600
3/8. That's where my 3[br]eights will be.
0:07:20.630,0:07:22.639
Let's have a look at[br]another one.
0:07:24.590,0:07:28.340
This time will look at
0:07:28.340,0:07:33.206
11 twelfths. So we need to[br]divide our line up into.
0:07:34.300,0:07:40.033
Pieces so we have 12 pieces[br]of equal size.
0:07:48.390,0:07:55.350
OK, so we wanted[br]eleven of them, so
0:07:55.350,0:08:02.310
we need to count[br]11 one 23456789 ten
0:08:02.310,0:08:05.790
11. So at 11
0:08:05.790,0:08:08.800
twelfths. Is represented there.
0:08:10.240,0:08:16.786
Let's look more[br]closely at our
0:08:16.786,0:08:18.968
fraction half.
0:08:20.040,0:08:26.088
Now we've already seen that half[br]is exactly the same as two
0:08:26.088,0:08:31.174
quarters. And it's exactly the[br]same as 36.
0:08:32.100,0:08:38.832
Well, it's also the same[br]as 4 eighths 5/10.
0:08:40.640,0:08:44.210
2040 deaths
0:08:45.600,0:08:50.770
9900 and 98th and so on. We[br]could go on.
0:08:51.500,0:08:58.116
And what we have[br]here is actually equivalent
0:08:58.116,0:09:05.376
fractions. Each one of these[br]fractions are equivalent at the
0:09:05.376,0:09:08.152
same as each other.
0:09:10.460,0:09:14.090
Now, this form of the fraction
0:09:14.090,0:09:20.985
half. Is our fraction in its[br]lowest form, and often we need
0:09:20.985,0:09:23.610
to write fractions in their
0:09:23.610,0:09:29.122
lowest form. It's much easier to[br]visualize them actually in this
0:09:29.122,0:09:32.118
lowest form than it is in any
0:09:32.118,0:09:36.355
other form. So we often want to[br]find the lowest form.
0:09:37.710,0:09:43.683
Well, let's have a look 1st at[br]finding some other equivalent
0:09:43.683,0:09:46.941
fractions. So let's say I take
0:09:46.941,0:09:52.485
3/4. How do I find an[br]equivalent fraction? Well, what
0:09:52.485,0:09:58.185
I can do is multiply the top[br]number and the bottom number.
0:09:59.270,0:10:00.878
By the same number.
0:10:01.380,0:10:05.258
So let's say I multiply by two.
0:10:05.870,0:10:10.719
If I multiply the top number by[br]two, I must also multiply the
0:10:10.719,0:10:14.822
bottom number by two so that I'm[br]not changing the fraction.
0:10:15.750,0:10:19.691
3 * 2 six 4 * 2
0:10:19.691,0:10:26.454
is 8. So 6 eighths[br]is a fraction equivalent to 3/4.
0:10:28.370,0:10:29.578
Let's try another one.
0:10:30.350,0:10:33.710
This time, let's take our 3/4.
0:10:34.440,0:10:39.434
And multiply it by three. The[br]top numbers multiplied by three,
0:10:39.434,0:10:45.336
so most the bottom number B3[br]threes and 9 three force or 12,
0:10:45.336,0:10:50.330
so nine twelfths is equivalent[br]to 6 eighths, and they're both
0:10:50.330,0:10:51.692
equivalent to 3/4.
0:10:53.070,0:10:57.437
Let's do one more this time.[br]Let's multiply both the top
0:10:57.437,0:11:02.598
number on the bottom number by[br]10. So we have 3 * 10.
0:11:03.350,0:11:04.718
Giving us 30.
0:11:05.230,0:11:11.260
And 4 * 10 giving us[br]40. So another fraction
0:11:11.260,0:11:14.878
equivalent to 3/4 is 3040[br]deaths.
0:11:16.090,0:11:20.743
So it's very easy to find[br]equivalent fractions as long as
0:11:20.743,0:11:25.819
you multiply the top number on[br]the bottom number by the same
0:11:25.819,0:11:29.203
number. Now we have some[br]mathematical language here.
0:11:29.203,0:11:34.279
Instead of using the word top[br]number and write it down top
0:11:34.279,0:11:38.668
number. And bottom[br]number.
0:11:40.730,0:11:45.720
We have two words that[br]we use. The top number
0:11:45.720,0:11:47.716
is called the numerator.
0:11:49.350,0:11:52.605
On the bottom number the
0:11:52.605,0:11:58.523
denominator. Now let's have a[br]look at seeing how we go the
0:11:58.523,0:12:03.176
other way. When we have an[br]equivalent fraction, how do we
0:12:03.176,0:12:05.714
find this fraction in its lowest
0:12:05.714,0:12:08.300
form? Well, let's look at an
0:12:08.300,0:12:13.419
example. Let's say we've[br]got 8, one, hundreds.
0:12:14.890,0:12:20.446
Now we need to find the number[br]that the lowest form was
0:12:20.446,0:12:24.815
multiplied by. And that we ended[br]up with eight one hundredths.
0:12:25.610,0:12:29.840
Well, the opposite of[br]multiplying is dividing, so we
0:12:29.840,0:12:34.540
need to divide both the[br]numerator and the denominator by
0:12:34.540,0:12:35.950
the same number.
0:12:36.460,0:12:40.132
So that we get back to a[br]fraction in its lowest form.
0:12:40.780,0:12:46.282
Well, if we look at the numbers[br]we have here 8 and 100, the
0:12:46.282,0:12:50.605
first thing you should notice is[br]actually the both even numbers.
0:12:51.130,0:12:54.710
And if they're both even[br]numbers, then obviously we can
0:12:54.710,0:12:56.500
divide them both by two.
0:12:57.380,0:13:03.188
So let's start by dividing the[br]numerator by two and the
0:13:03.188,0:13:04.772
denominator by two.
0:13:05.510,0:13:11.850
8 / 2 is four 100[br]/ 2 is 50.
0:13:12.970,0:13:17.002
Now we need to look at our[br]fraction. Again. We found an
0:13:17.002,0:13:20.026
equivalent fraction, but is it[br]in its lowest form?
0:13:20.830,0:13:25.241
Well again, we can see that[br]they're both even numbers, both
0:13:25.241,0:13:30.053
4 and 50 even, and so we can[br]divide by two again.
0:13:30.560,0:13:38.100
4 / 4 gives us[br]2 and 50 / 2.
0:13:38.750,0:13:44.100
Gives us 25, so another[br]equivalent fraction, but is it
0:13:44.100,0:13:46.240
in its lowest form?
0:13:46.960,0:13:53.330
Well, we need to see if there is[br]any number that goes both into
0:13:53.330,0:13:56.970
the numerator and the[br]denominator. Well, the only
0:13:56.970,0:14:02.430
numbers that go into 2A one[br]which goes into all numbers, so
0:14:02.430,0:14:09.255
that's not going to help us. And[br]two now 2 doesn't go into 25. So
0:14:09.255,0:14:14.715
therefore we found the fraction[br]in its lowest form, so 8 one
0:14:14.715,0:14:17.445
hundreds. The lowest form is 220
0:14:17.445,0:14:23.476
fifths. So when a fraction is in[br]its lowest form, the only number
0:14:23.476,0:14:27.744
that will go into both the[br]numerator and the denominator is
0:14:27.744,0:14:31.360
one. Those numbers have no other
0:14:31.360,0:14:37.375
common factor. Now if we look[br]here, we can see that in fact.
0:14:37.950,0:14:41.910
We could have divided by 4.
0:14:41.910,0:14:45.474
Straight away, instead of[br]dividing by two twice, well,
0:14:45.474,0:14:49.434
that's fine. If you've notice[br]tthat for was a factor.
0:14:49.990,0:14:54.577
Of both the numerator and the[br]denominator, you could have gone
0:14:54.577,0:15:01.249
straight there doing 8 / 4 was[br]two and 100 / 4 was 25 and then
0:15:01.249,0:15:06.670
check to see if you were in the[br]lowest form. That's fine, but
0:15:06.670,0:15:11.052
often. With numbers, larger[br]numbers is not always easy to
0:15:11.052,0:15:15.100
see what the highest common[br]factor is of these two numbers,
0:15:15.100,0:15:18.044
the numerator and the[br]denominator. So often it's
0:15:18.044,0:15:22.092
easier to work down to some[br]smaller numbers, and then you
0:15:22.092,0:15:25.772
can be certain that there are no[br]other common factors.
0:15:28.020,0:15:28.540
Now.
0:15:29.880,0:15:33.516
If we take all the[br]pieces of a fraction
0:15:33.516,0:15:37.152
like I did with my[br]chocolate, I took all
0:15:37.152,0:15:38.364
six of them.
0:15:39.760,0:15:43.596
That's the same as 6 / 6.
0:15:44.110,0:15:45.590
And that was our whole.
0:15:47.430,0:15:53.406
And any whole number can be[br]written this way, so we could
0:15:53.406,0:15:59.561
have. 3 thirds if we take all[br]the pieces, we've got one.
0:15:59.870,0:16:05.865
8 eighths, if we take all the[br]pieces, we've got one.
0:16:05.870,0:16:09.340
Now I'm going to rewrite.
0:16:09.900,0:16:13.239
Mathematical words numerator.
0:16:13.790,0:16:17.438
Divided fight denominator.
0:16:18.530,0:16:22.270
Because we're now going to
0:16:22.270,0:16:28.190
look. Add fractions[br]where the numerator.
0:16:30.490,0:16:33.938
Smaller than the denominator.
0:16:36.590,0:16:41.378
And we have a name for these[br]type of fractions and they
0:16:41.378,0:16:42.575
called proper fractions.
0:16:47.530,0:16:50.860
And examples.
0:16:50.860,0:16:52.330
Half.
0:16:53.320,0:16:58.140
3/4[br]16
0:16:59.380,0:17:06.660
7/8 5/10 and[br]seeing all these cases, the
0:17:06.660,0:17:10.060
numerator is smaller number than
0:17:10.060,0:17:16.410
the denominator. And as long as[br]that is the case, then we have a
0:17:16.410,0:17:20.730
proper fraction so we can have[br]any numbers 100 hundred and 50th
0:17:20.730,0:17:24.554
for example. Now if
0:17:24.554,0:17:30.700
the numerator.[br]Is greater than
0:17:30.700,0:17:32.820
the denominator?
0:17:36.980,0:17:41.556
Then the fraction is called[br]an improper fraction.
0:17:47.160,0:17:50.289
And some examples.
0:17:50.350,0:17:53.098
Three over two or three halfs.
0:17:53.930,0:17:59.490
7 fifths.[br]Eight quarters
0:18:00.960,0:18:03.650
We could have 12 bytes.
0:18:05.120,0:18:08.708
Or we could have 201 hundredths.
0:18:09.780,0:18:14.873
And in all these cases, the[br]numerator is larger than the
0:18:14.873,0:18:19.590
denominator. And it shows that[br]what we've got is actually more
0:18:19.590,0:18:20.619
than whole 1.
0:18:21.540,0:18:26.090
All these fractions, the[br]proper ones are smaller than a
0:18:26.090,0:18:31.095
whole one. We haven't taken[br]all of the pieces 3/4. We've
0:18:31.095,0:18:37.465
only taken 3 out of the four[br]161 out of the six, so that
0:18:37.465,0:18:41.560
all smaller than a whole one[br]with improper fractions.
0:18:42.790,0:18:45.052
They are all larger than one
0:18:45.052,0:18:50.866
whole 1. So if we take three[br]over 2 for example, what we've
0:18:50.866,0:18:52.896
actually got is 3 halfs.
0:18:54.790,0:18:58.993
Oh, improper fractions can be[br]written in this form.
0:18:59.730,0:19:05.466
All they can be written[br]as mixed fractions.
0:19:08.280,0:19:12.753
So let's have a look[br]at our three halfs.
0:19:14.450,0:19:19.078
And what we can do is put two[br]hearts together to make the
0:19:19.078,0:19:25.392
whole 1. And we've got 1/2 left[br]over, so that can be written as
0:19:25.392,0:19:26.976
one and a half.
0:19:28.040,0:19:32.324
So there are exactly the same,[br]but written in a different form
0:19:32.324,0:19:34.109
1 as a mixed fraction.
0:19:34.620,0:19:39.714
And one other top heavy[br]fraction, an improper fraction
0:19:39.714,0:19:44.242
where the numerator is larger[br]than the denominator.
0:19:46.390,0:19:48.202
Let's have a look at another
0:19:48.202,0:19:53.906
example. Let's say we[br]had 8 thirds.
0:19:53.910,0:19:55.238
This out the way.
0:19:56.780,0:20:00.320
Let's count
0:20:00.320,0:20:05.790
out 1234567.[br]8 thirds
0:20:06.900,0:20:11.047
How else can we write that?[br]How do we write that as a
0:20:11.047,0:20:11.685
mixed fraction?
0:20:13.110,0:20:16.140
Well, what we're looking[br]for is how many whole ones
0:20:16.140,0:20:17.049
we've got there.
0:20:18.310,0:20:22.398
Well, if something's been[br]divided into 3 pieces.
0:20:23.420,0:20:26.150
It takes 3 pieces to make the
0:20:26.150,0:20:28.760
whole 1. So that's one whole 1.
0:20:30.510,0:20:34.026
There we have another whole 12.
0:20:34.890,0:20:42.114
And we've got 2/3 left over,[br]so 8 thirds is exactly the
0:20:42.114,0:20:45.124
same as two and 2/3.
0:20:48.770,0:20:50.710
Let's look at one more.
0:20:51.710,0:20:55.485
Let's say we had Seven
0:20:55.485,0:21:00.999
quarters. Now we know that there[br]are four quarters in each hole,
0:21:00.999,0:21:06.446
one. So we see how many fours go[br]into Seven. Well, that's one.
0:21:06.960,0:21:13.080
And we've got 3 left over, so[br]we've got one and 3/4.
0:21:14.180,0:21:16.784
Let's have a look at one more.
0:21:18.090,0:21:21.300
37 tenths
0:21:22.920,0:21:27.892
Now we've split something up[br]into 10 pieces of equal size.
0:21:28.930,0:21:34.030
So we need 10 of those to make a[br]whole one, so we need to see how
0:21:34.030,0:21:37.030
many 10s, how many whole ones[br]there are in 37.
0:21:38.130,0:21:43.267
Well, three 10s makes 30, so[br]that's three whole ones, and
0:21:43.267,0:21:47.937
we've got 7 leftover, so we've[br]got 3 and 7/10.
0:21:49.020,0:21:52.426
Just move
0:21:52.426,0:21:59.202
those. Now let's have[br]a look at doing the reverse
0:21:59.202,0:22:05.676
process. So if we start with a[br]mixed fraction, how do we turn
0:22:05.676,0:22:08.166
it into an improper fraction?
0:22:08.740,0:22:11.902
Let's look at three and a
0:22:11.902,0:22:16.498
quarter. And if we look at this[br]visually, we've got.
0:22:17.170,0:22:18.658
3 hole once.
0:22:20.540,0:22:23.870
And one quarter.
0:22:27.500,0:22:29.432
And what we want to turn it
0:22:29.432,0:22:33.599
into. Is all[br]quarters.
0:22:34.640,0:22:36.470
So we have a whole 1.
0:22:37.360,0:22:43.769
And if we split it into[br]quarters, we know that a whole 1
0:22:43.769,0:22:45.248
needs four quarters.
0:22:45.770,0:22:47.280
So we have four there.
0:22:47.810,0:22:49.118
Another for their.
0:22:49.680,0:22:52.680
Another folder plus this one.
0:22:53.310,0:22:56.124
So we've got three force or 12.
0:22:56.640,0:23:04.032
Plus the one gives us 13[br]quarters, so 3 1/4 is exactly
0:23:04.032,0:23:07.112
the same as 13 quarters.
0:23:07.660,0:23:12.423
Well, let's have a look at how[br]you might do this.
0:23:14.000,0:23:15.500
If you haven't got the visual
0:23:15.500,0:23:21.500
aid. Well, what we've actually[br]got here is our whole number.
0:23:22.550,0:23:23.639
And the fraction.
0:23:24.240,0:23:25.940
We wanted in quarters.
0:23:27.070,0:23:30.686
So what we're doing[br]is right it again.
0:23:31.920,0:23:36.550
We're actually saying We want[br]four quarters for every hole
0:23:36.550,0:23:39.791
one, so we've got three lots of
0:23:39.791,0:23:44.910
four. And then what were[br]ranting on is our one, and
0:23:44.910,0:23:46.378
these are all quarters.
0:23:47.600,0:23:51.425
So it's the whole number[br]multiplied by the denominator.
0:23:52.460,0:23:56.930
We've added the extra that[br]we have here. Whatever this
0:23:56.930,0:24:01.400
number is, and those are the[br]number of quarters we've
0:24:01.400,0:24:07.211
got. So we've got our 3/4 of[br]12 + 1/4, so 13 quarters.
0:24:08.940,0:24:10.956
Let's have a look at one more
0:24:10.956,0:24:16.478
example. Let's say we've got[br]five and two ninths.
0:24:18.310,0:24:21.086
We want to turn it[br]into this format.
0:24:22.360,0:24:28.632
Ninths well, if we want to take[br]a whole one, we wouldn't need 9
0:24:28.632,0:24:34.904
ninths and we've got five whole[br]ones, so we're going to have 5 *
0:24:34.904,0:24:37.592
9 lots of 9th this time.
0:24:38.250,0:24:42.660
And then we need to add on the[br]two nights that we have here.
0:24:42.670,0:24:50.530
So 5 nines of 45 plus[br]the two and that all 9th.
0:24:50.530,0:24:53.805
So we have 47 ninths.
0:24:57.170,0:25:00.734
Any whole number can be written[br]as a fraction.
0:25:01.270,0:25:04.078
So for example, if we take[br]the number 2.
0:25:05.930,0:25:10.097
If we write it with the[br]denominator of one.
0:25:11.580,0:25:13.860
We've written it as a fraction.
0:25:15.050,0:25:20.143
And any equivalent form, so we[br]could have 4 over 2.
0:25:20.770,0:25:24.370
30 over
0:25:24.370,0:25:31.193
15. And so on.[br]So any whole number can be
0:25:31.193,0:25:35.963
written as a fraction with a[br]numerator and a denominator.
0:25:37.560,0:25:45.186
So fractions.[br]They can appear in a number
0:25:45.186,0:25:50.460
of different forms. You might[br]see proper fractions, improper
0:25:50.460,0:25:52.218
fractions, mixed fractions.
0:25:53.060,0:25:57.272
And you can see lots of[br]different equivalent fractions.
0:25:57.870,0:26:00.255
So that all different[br]ways that we see them.