WEBVTT
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This tutorial is about the basic
concepts of fractions.
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What they are, what they look
like, and why we have them.
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A function is a way of writing
part of a whole.
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And it's formed when we divide a
whole into an equal number of
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pieces. Now let's have a look.
I've got a representation here.
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Of a whole.
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And let's say we want to divide
it into 4 equal pieces.
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So there we've
taken 1 hole
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and divided it
into 4 equal
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pieces. So each
piece represents 1/4.
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Wow.
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I've now taken 1/4 away.
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Now I've removed
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two quarters. If
I take a third.
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That's 3/4.
And if I take the false so I've
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now got all four pieces.
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I've taken all of them for
quarters, which is exactly the
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same as taking the whole.
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Let's just return for a moment
to the two quarters.
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Now
two
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quarters. Is exactly
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the same. As if I'd started
with my whole and actually
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divided it into.
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2 pieces of equal size.
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And you can see that that's
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exactly the same. As two
quarters so I can write two
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quarters. As one
half.
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Let's have a look at
another illustration now.
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Here I have a bar of chocolate.
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It's been divided.
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Into six pieces of equal size.
So we've taken a whole bar and
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divide it into six pieces.
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So each piece is
16.
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Now, let's say I'm going to
share my bar of chocolate with
00:02:42.506 --> 00:02:43.550
the camera man.
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So I want to divide the bar
of chocolate into two pieces.
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So if I do that.
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Where each going to have one
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236. So 1/2 is
exactly the same as 36.
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But there's not just one
cameraman. We've got two
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cameramen, so I need to share
it. Actually, between three of
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us. So now if I put my bar back
together and I need to share it
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between 3:00. Where
each going to get.
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Two pieces.
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So 1/3 is exactly the
same as 26.
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But Let's say I
want to eat all my chocolate bar
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myself, so I'm going to have all
six pieces, so they're all mine.
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Not going to share them, so I
take all six pieces.
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And I've taken away the whole
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bar.
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So.
Fractions we can look at.
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In two ways.
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We can look at it as the number
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of pieces. That we've used.
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Divided by the
number of pieces.
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That make a whole.
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Oh
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As the whole.
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Divided by. Number of pieces
or number of people that we've
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divided it into.
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So here we have a whole bar
divided into 6 pieces.
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Here we have the number of
pieces that we've taken divided
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note 5 the number of pieces that
make up the whole bar.
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Let's have a look
at some other fractions.
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Let's say
we have
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3/8.
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So we've divided a whole up into
8 pieces of equal size.
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And we've taken three of them.
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3/8
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We could have 11 twelfths.
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So we've divided a whole up into
12 pieces and taking eleven of
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them. We could have
7/10.
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Here we will have divided a hole
into 10 pieces of equal size and
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taken Seven of them.
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And we can have.
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Any numbers in our fraction so
we could have 105 hundreds or
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three 167th and so on.
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Now we've looked at representing
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fractions. Using piece of Cod
circular representation are
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rectangle with our bar of
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chocolate. Let's have a look at
one more before we move on and
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let's let's see it on.
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A section of number line.
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So let's say we have zero here.
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And one here.
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So let's look at what 3/8 might
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look like. While I need to
divide my section into 8 pieces
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of equal size.
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Now obviously this is an
illustration, so I'm not
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actually getting my router
out to make sure I've got
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equal size pieces.
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But hopefully. That's about
right. So we've got 12345678
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pieces of equal size and I'm
going to take three of them.
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So if I take 1, two
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3/8. That's where my 3
eights will be.
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Let's have a look at
another one.
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This time will look at
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11 twelfths. So we need to
divide our line up into.
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Pieces so we have 12 pieces
of equal size.
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OK, so we wanted
eleven of them, so
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we need to count
11 one 23456789 ten
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11. So at 11
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twelfths. Is represented there.
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Let's look more
closely at our
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fraction half.
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Now we've already seen that half
is exactly the same as two
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quarters. And it's exactly the
same as 36.
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Well, it's also the same
as 4 eighths 5/10.
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2040 deaths
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9900 and 98th and so on. We
could go on.
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And what we have
here is actually equivalent
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fractions. Each one of these
fractions are equivalent at the
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same as each other.
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Now, this form of the fraction
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half. Is our fraction in its
lowest form, and often we need
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to write fractions in their
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lowest form. It's much easier to
visualize them actually in this
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lowest form than it is in any
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other form. So we often want to
find the lowest form.
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Well, let's have a look 1st at
finding some other equivalent
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fractions. So let's say I take
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3/4. How do I find an
equivalent fraction? Well, what
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I can do is multiply the top
number and the bottom number.
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By the same number.
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So let's say I multiply by two.
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If I multiply the top number by
two, I must also multiply the
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bottom number by two so that I'm
not changing the fraction.
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3 * 2 six 4 * 2
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is 8. So 6 eighths
is a fraction equivalent to 3/4.
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Let's try another one.
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This time, let's take our 3/4.
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And multiply it by three. The
top numbers multiplied by three,
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so most the bottom number B3
threes and 9 three force or 12,
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so nine twelfths is equivalent
to 6 eighths, and they're both
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equivalent to 3/4.
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Let's do one more this time.
Let's multiply both the top
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number on the bottom number by
10. So we have 3 * 10.
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Giving us 30.
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And 4 * 10 giving us
40. So another fraction
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equivalent to 3/4 is 3040
deaths.
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So it's very easy to find
equivalent fractions as long as
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you multiply the top number on
the bottom number by the same
00:11:25.819 --> 00:11:29.203
number. Now we have some
mathematical language here.
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Instead of using the word top
number and write it down top
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number. And bottom
number.
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We have two words that
we use. The top number
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is called the numerator.
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On the bottom number the
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denominator. Now let's have a
look at seeing how we go the
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other way. When we have an
equivalent fraction, how do we
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find this fraction in its lowest
00:12:05.714 --> 00:12:08.300
form? Well, let's look at an
00:12:08.300 --> 00:12:13.419
example. Let's say we've
got 8, one, hundreds.
00:12:14.890 --> 00:12:20.446
Now we need to find the number
that the lowest form was
00:12:20.446 --> 00:12:24.815
multiplied by. And that we ended
up with eight one hundredths.
00:12:25.610 --> 00:12:29.840
Well, the opposite of
multiplying is dividing, so we
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need to divide both the
numerator and the denominator by
00:12:34.540 --> 00:12:35.950
the same number.
00:12:36.460 --> 00:12:40.132
So that we get back to a
fraction in its lowest form.
00:12:40.780 --> 00:12:46.282
Well, if we look at the numbers
we have here 8 and 100, the
00:12:46.282 --> 00:12:50.605
first thing you should notice is
actually the both even numbers.
00:12:51.130 --> 00:12:54.710
And if they're both even
numbers, then obviously we can
00:12:54.710 --> 00:12:56.500
divide them both by two.
00:12:57.380 --> 00:13:03.188
So let's start by dividing the
numerator by two and the
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denominator by two.
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8 / 2 is four 100
/ 2 is 50.
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Now we need to look at our
fraction. Again. We found an
00:13:17.002 --> 00:13:20.026
equivalent fraction, but is it
in its lowest form?
00:13:20.830 --> 00:13:25.241
Well again, we can see that
they're both even numbers, both
00:13:25.241 --> 00:13:30.053
4 and 50 even, and so we can
divide by two again.
00:13:30.560 --> 00:13:38.100
4 / 4 gives us
2 and 50 / 2.
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Gives us 25, so another
equivalent fraction, but is it
00:13:44.100 --> 00:13:46.240
in its lowest form?
00:13:46.960 --> 00:13:53.330
Well, we need to see if there is
any number that goes both into
00:13:53.330 --> 00:13:56.970
the numerator and the
denominator. Well, the only
00:13:56.970 --> 00:14:02.430
numbers that go into 2A one
which goes into all numbers, so
00:14:02.430 --> 00:14:09.255
that's not going to help us. And
two now 2 doesn't go into 25. So
00:14:09.255 --> 00:14:14.715
therefore we found the fraction
in its lowest form, so 8 one
00:14:14.715 --> 00:14:17.445
hundreds. The lowest form is 220
00:14:17.445 --> 00:14:23.476
fifths. So when a fraction is in
its lowest form, the only number
00:14:23.476 --> 00:14:27.744
that will go into both the
numerator and the denominator is
00:14:27.744 --> 00:14:31.360
one. Those numbers have no other
00:14:31.360 --> 00:14:37.375
common factor. Now if we look
here, we can see that in fact.
00:14:37.950 --> 00:14:41.910
We could have divided by 4.
00:14:41.910 --> 00:14:45.474
Straight away, instead of
dividing by two twice, well,
00:14:45.474 --> 00:14:49.434
that's fine. If you've notice
tthat for was a factor.
00:14:49.990 --> 00:14:54.577
Of both the numerator and the
denominator, you could have gone
00:14:54.577 --> 00:15:01.249
straight there doing 8 / 4 was
two and 100 / 4 was 25 and then
00:15:01.249 --> 00:15:06.670
check to see if you were in the
lowest form. That's fine, but
00:15:06.670 --> 00:15:11.052
often. With numbers, larger
numbers is not always easy to
00:15:11.052 --> 00:15:15.100
see what the highest common
factor is of these two numbers,
00:15:15.100 --> 00:15:18.044
the numerator and the
denominator. So often it's
00:15:18.044 --> 00:15:22.092
easier to work down to some
smaller numbers, and then you
00:15:22.092 --> 00:15:25.772
can be certain that there are no
other common factors.
00:15:28.020 --> 00:15:28.540
Now.
00:15:29.880 --> 00:15:33.516
If we take all the
pieces of a fraction
00:15:33.516 --> 00:15:37.152
like I did with my
chocolate, I took all
00:15:37.152 --> 00:15:38.364
six of them.
00:15:39.760 --> 00:15:43.596
That's the same as 6 / 6.
00:15:44.110 --> 00:15:45.590
And that was our whole.
00:15:47.430 --> 00:15:53.406
And any whole number can be
written this way, so we could
00:15:53.406 --> 00:15:59.561
have. 3 thirds if we take all
the pieces, we've got one.
00:15:59.870 --> 00:16:05.865
8 eighths, if we take all the
pieces, we've got one.
00:16:05.870 --> 00:16:09.340
Now I'm going to rewrite.
00:16:09.900 --> 00:16:13.239
Mathematical words numerator.
00:16:13.790 --> 00:16:17.438
Divided fight denominator.
00:16:18.530 --> 00:16:22.270
Because we're now going to
00:16:22.270 --> 00:16:28.190
look. Add fractions
where the numerator.
00:16:30.490 --> 00:16:33.938
Smaller than the denominator.
00:16:36.590 --> 00:16:41.378
And we have a name for these
type of fractions and they
00:16:41.378 --> 00:16:42.575
called proper fractions.
00:16:47.530 --> 00:16:50.860
And examples.
00:16:50.860 --> 00:16:52.330
Half.
00:16:53.320 --> 00:16:58.140
3/4
16
00:16:59.380 --> 00:17:06.660
7/8 5/10 and
seeing all these cases, the
00:17:06.660 --> 00:17:10.060
numerator is smaller number than
00:17:10.060 --> 00:17:16.410
the denominator. And as long as
that is the case, then we have a
00:17:16.410 --> 00:17:20.730
proper fraction so we can have
any numbers 100 hundred and 50th
00:17:20.730 --> 00:17:24.554
for example. Now if
00:17:24.554 --> 00:17:30.700
the numerator.
Is greater than
00:17:30.700 --> 00:17:32.820
the denominator?
00:17:36.980 --> 00:17:41.556
Then the fraction is called
an improper fraction.
00:17:47.160 --> 00:17:50.289
And some examples.
00:17:50.350 --> 00:17:53.098
Three over two or three halfs.
00:17:53.930 --> 00:17:59.490
7 fifths.
Eight quarters
00:18:00.960 --> 00:18:03.650
We could have 12 bytes.
00:18:05.120 --> 00:18:08.708
Or we could have 201 hundredths.
00:18:09.780 --> 00:18:14.873
And in all these cases, the
numerator is larger than the
00:18:14.873 --> 00:18:19.590
denominator. And it shows that
what we've got is actually more
00:18:19.590 --> 00:18:20.619
than whole 1.
00:18:21.540 --> 00:18:26.090
All these fractions, the
proper ones are smaller than a
00:18:26.090 --> 00:18:31.095
whole one. We haven't taken
all of the pieces 3/4. We've
00:18:31.095 --> 00:18:37.465
only taken 3 out of the four
161 out of the six, so that
00:18:37.465 --> 00:18:41.560
all smaller than a whole one
with improper fractions.
00:18:42.790 --> 00:18:45.052
They are all larger than one
00:18:45.052 --> 00:18:50.866
whole 1. So if we take three
over 2 for example, what we've
00:18:50.866 --> 00:18:52.896
actually got is 3 halfs.
00:18:54.790 --> 00:18:58.993
Oh, improper fractions can be
written in this form.
00:18:59.730 --> 00:19:05.466
All they can be written
as mixed fractions.
00:19:08.280 --> 00:19:12.753
So let's have a look
at our three halfs.
00:19:14.450 --> 00:19:19.078
And what we can do is put two
hearts together to make the
00:19:19.078 --> 00:19:25.392
whole 1. And we've got 1/2 left
over, so that can be written as
00:19:25.392 --> 00:19:26.976
one and a half.
00:19:28.040 --> 00:19:32.324
So there are exactly the same,
but written in a different form
00:19:32.324 --> 00:19:34.109
1 as a mixed fraction.
00:19:34.620 --> 00:19:39.714
And one other top heavy
fraction, an improper fraction
00:19:39.714 --> 00:19:44.242
where the numerator is larger
than the denominator.
00:19:46.390 --> 00:19:48.202
Let's have a look at another
00:19:48.202 --> 00:19:53.906
example. Let's say we
had 8 thirds.
00:19:53.910 --> 00:19:55.238
This out the way.
00:19:56.780 --> 00:20:00.320
Let's count
00:20:00.320 --> 00:20:05.790
out 1234567.
8 thirds
00:20:06.900 --> 00:20:11.047
How else can we write that?
How do we write that as a
00:20:11.047 --> 00:20:11.685
mixed fraction?
00:20:13.110 --> 00:20:16.140
Well, what we're looking
for is how many whole ones
00:20:16.140 --> 00:20:17.049
we've got there.
00:20:18.310 --> 00:20:22.398
Well, if something's been
divided into 3 pieces.
00:20:23.420 --> 00:20:26.150
It takes 3 pieces to make the
00:20:26.150 --> 00:20:28.760
whole 1. So that's one whole 1.
00:20:30.510 --> 00:20:34.026
There we have another whole 12.
00:20:34.890 --> 00:20:42.114
And we've got 2/3 left over,
so 8 thirds is exactly the
00:20:42.114 --> 00:20:45.124
same as two and 2/3.
00:20:48.770 --> 00:20:50.710
Let's look at one more.
00:20:51.710 --> 00:20:55.485
Let's say we had Seven
00:20:55.485 --> 00:21:00.999
quarters. Now we know that there
are four quarters in each hole,
00:21:00.999 --> 00:21:06.446
one. So we see how many fours go
into Seven. Well, that's one.
00:21:06.960 --> 00:21:13.080
And we've got 3 left over, so
we've got one and 3/4.
00:21:14.180 --> 00:21:16.784
Let's have a look at one more.
00:21:18.090 --> 00:21:21.300
37 tenths
00:21:22.920 --> 00:21:27.892
Now we've split something up
into 10 pieces of equal size.
00:21:28.930 --> 00:21:34.030
So we need 10 of those to make a
whole one, so we need to see how
00:21:34.030 --> 00:21:37.030
many 10s, how many whole ones
there are in 37.
00:21:38.130 --> 00:21:43.267
Well, three 10s makes 30, so
that's three whole ones, and
00:21:43.267 --> 00:21:47.937
we've got 7 leftover, so we've
got 3 and 7/10.
00:21:49.020 --> 00:21:52.426
Just move
00:21:52.426 --> 00:21:59.202
those. Now let's have
a look at doing the reverse
00:21:59.202 --> 00:22:05.676
process. So if we start with a
mixed fraction, how do we turn
00:22:05.676 --> 00:22:08.166
it into an improper fraction?
00:22:08.740 --> 00:22:11.902
Let's look at three and a
00:22:11.902 --> 00:22:16.498
quarter. And if we look at this
visually, we've got.
00:22:17.170 --> 00:22:18.658
3 hole once.
00:22:20.540 --> 00:22:23.870
And one quarter.
00:22:27.500 --> 00:22:29.432
And what we want to turn it
00:22:29.432 --> 00:22:33.599
into. Is all
quarters.
00:22:34.640 --> 00:22:36.470
So we have a whole 1.
00:22:37.360 --> 00:22:43.769
And if we split it into
quarters, we know that a whole 1
00:22:43.769 --> 00:22:45.248
needs four quarters.
00:22:45.770 --> 00:22:47.280
So we have four there.
00:22:47.810 --> 00:22:49.118
Another for their.
00:22:49.680 --> 00:22:52.680
Another folder plus this one.
00:22:53.310 --> 00:22:56.124
So we've got three force or 12.
00:22:56.640 --> 00:23:04.032
Plus the one gives us 13
quarters, so 3 1/4 is exactly
00:23:04.032 --> 00:23:07.112
the same as 13 quarters.
00:23:07.660 --> 00:23:12.423
Well, let's have a look at how
you might do this.
00:23:14.000 --> 00:23:15.500
If you haven't got the visual
00:23:15.500 --> 00:23:21.500
aid. Well, what we've actually
got here is our whole number.
00:23:22.550 --> 00:23:23.639
And the fraction.
00:23:24.240 --> 00:23:25.940
We wanted in quarters.
00:23:27.070 --> 00:23:30.686
So what we're doing
is right it again.
00:23:31.920 --> 00:23:36.550
We're actually saying We want
four quarters for every hole
00:23:36.550 --> 00:23:39.791
one, so we've got three lots of
00:23:39.791 --> 00:23:44.910
four. And then what were
ranting on is our one, and
00:23:44.910 --> 00:23:46.378
these are all quarters.
00:23:47.600 --> 00:23:51.425
So it's the whole number
multiplied by the denominator.
00:23:52.460 --> 00:23:56.930
We've added the extra that
we have here. Whatever this
00:23:56.930 --> 00:24:01.400
number is, and those are the
number of quarters we've
00:24:01.400 --> 00:24:07.211
got. So we've got our 3/4 of
12 + 1/4, so 13 quarters.
00:24:08.940 --> 00:24:10.956
Let's have a look at one more
00:24:10.956 --> 00:24:16.478
example. Let's say we've got
five and two ninths.
00:24:18.310 --> 00:24:21.086
We want to turn it
into this format.
00:24:22.360 --> 00:24:28.632
Ninths well, if we want to take
a whole one, we wouldn't need 9
00:24:28.632 --> 00:24:34.904
ninths and we've got five whole
ones, so we're going to have 5 *
00:24:34.904 --> 00:24:37.592
9 lots of 9th this time.
00:24:38.250 --> 00:24:42.660
And then we need to add on the
two nights that we have here.
00:24:42.670 --> 00:24:50.530
So 5 nines of 45 plus
the two and that all 9th.
00:24:50.530 --> 00:24:53.805
So we have 47 ninths.
00:24:57.170 --> 00:25:00.734
Any whole number can be written
as a fraction.
00:25:01.270 --> 00:25:04.078
So for example, if we take
the number 2.
00:25:05.930 --> 00:25:10.097
If we write it with the
denominator of one.
00:25:11.580 --> 00:25:13.860
We've written it as a fraction.
00:25:15.050 --> 00:25:20.143
And any equivalent form, so we
could have 4 over 2.
00:25:20.770 --> 00:25:24.370
30 over
00:25:24.370 --> 00:25:31.193
15. And so on.
So any whole number can be
00:25:31.193 --> 00:25:35.963
written as a fraction with a
numerator and a denominator.
00:25:37.560 --> 00:25:45.186
So fractions.
They can appear in a number
00:25:45.186 --> 00:25:50.460
of different forms. You might
see proper fractions, improper
00:25:50.460 --> 00:25:52.218
fractions, mixed fractions.
00:25:53.060 --> 00:25:57.272
And you can see lots of
different equivalent fractions.
00:25:57.870 --> 00:26:00.255
So that all different
ways that we see them.