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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

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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

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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

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form? Well, let's look at an

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example. Let's say we've
got 8, one, hundreds.

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Now we need to find the number
that the lowest form was

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multiplied by. And that we ended
up with eight one hundredths.

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Well, the opposite of
multiplying is dividing, so we

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need to divide both the
numerator and the denominator by

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the same number.

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So that we get back to a
fraction in its lowest form.

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Well, if we look at the numbers
we have here 8 and 100, the

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first thing you should notice is
actually the both even numbers.

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And if they're both even
numbers, then obviously we can

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divide them both by two.

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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

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equivalent fraction, but is it
in its lowest form?

169
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Well again, we can see that
they're both even numbers, both

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4 and 50 even, and so we can
divide by two again.

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4 / 4 gives us
2 and 50 / 2.

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Gives us 25, so another
equivalent fraction, but is it

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in its lowest form?

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Well, we need to see if there is
any number that goes both into

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the numerator and the
denominator. Well, the only

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numbers that go into 2A one
which goes into all numbers, so

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that's not going to help us. And
two now 2 doesn't go into 25. So

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therefore we found the fraction
in its lowest form, so 8 one

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hundreds. The lowest form is 220

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fifths. So when a fraction is in
its lowest form, the only number

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that will go into both the
numerator and the denominator is

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one. Those numbers have no other

183
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common factor. Now if we look
here, we can see that in fact.

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We could have divided by 4.

185
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Straight away, instead of
dividing by two twice, well,

186
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that's fine. If you've notice
tthat for was a factor.

187
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Of both the numerator and the
denominator, you could have gone

188
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straight there doing 8 / 4 was
two and 100 / 4 was 25 and then

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check to see if you were in the
lowest form. That's fine, but

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often. With numbers, larger
numbers is not always easy to

191
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see what the highest common
factor is of these two numbers,

192
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the numerator and the
denominator. So often it's

193
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easier to work down to some
smaller numbers, and then you

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can be certain that there are no
other common factors.

195
00:15:28,020 --> 00:15:28,540
Now.

196
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If we take all the
pieces of a fraction

197
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like I did with my
chocolate, I took all

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00:15:37,152 --> 00:15:38,364
six of them.

199
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That's the same as 6 / 6.

200
00:15:44,110 --> 00:15:45,590
And that was our whole.

201
00:15:47,430 --> 00:15:53,406
And any whole number can be
written this way, so we could

202
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have. 3 thirds if we take all
the pieces, we've got one.

203
00:15:59,870 --> 00:16:05,865
8 eighths, if we take all the
pieces, we've got one.

204
00:16:05,870 --> 00:16:09,340
Now I'm going to rewrite.

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00:16:09,900 --> 00:16:13,239
Mathematical words numerator.

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00:16:13,790 --> 00:16:17,438
Divided fight denominator.

207
00:16:18,530 --> 00:16:22,270
Because we're now going to

208
00:16:22,270 --> 00:16:28,190
look. Add fractions
where the numerator.

209
00:16:30,490 --> 00:16:33,938
Smaller than the denominator.

210
00:16:36,590 --> 00:16:41,378
And we have a name for these
type of fractions and they

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called proper fractions.

212
00:16:47,530 --> 00:16:50,860
And examples.

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00:16:50,860 --> 00:16:52,330
Half.

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3/4
16

215
00:16:59,380 --> 00:17:06,660
7/8 5/10 and
seeing all these cases, the

216
00:17:06,660 --> 00:17:10,060
numerator is smaller number than

217
00:17:10,060 --> 00:17:16,410
the denominator. And as long as
that is the case, then we have a

218
00:17:16,410 --> 00:17:20,730
proper fraction so we can have
any numbers 100 hundred and 50th

219
00:17:20,730 --> 00:17:24,554
for example. Now if

220
00:17:24,554 --> 00:17:30,700
the numerator.
Is greater than

221
00:17:30,700 --> 00:17:32,820
the denominator?

222
00:17:36,980 --> 00:17:41,556
Then the fraction is called
an improper fraction.

223
00:17:47,160 --> 00:17:50,289
And some examples.

224
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Three over two or three halfs.

225
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7 fifths.
Eight quarters

226
00:18:00,960 --> 00:18:03,650
We could have 12 bytes.

227
00:18:05,120 --> 00:18:08,708
Or we could have 201 hundredths.

228
00:18:09,780 --> 00:18:14,873
And in all these cases, the
numerator is larger than the

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denominator. And it shows that
what we've got is actually more

230
00:18:19,590 --> 00:18:20,619
than whole 1.

231
00:18:21,540 --> 00:18:26,090
All these fractions, the
proper ones are smaller than a

232
00:18:26,090 --> 00:18:31,095
whole one. We haven't taken
all of the pieces 3/4. We've

233
00:18:31,095 --> 00:18:37,465
only taken 3 out of the four
161 out of the six, so that

234
00:18:37,465 --> 00:18:41,560
all smaller than a whole one
with improper fractions.

235
00:18:42,790 --> 00:18:45,052
They are all larger than one

236
00:18:45,052 --> 00:18:50,866
whole 1. So if we take three
over 2 for example, what we've

237
00:18:50,866 --> 00:18:52,896
actually got is 3 halfs.

238
00:18:54,790 --> 00:18:58,993
Oh, improper fractions can be
written in this form.

239
00:18:59,730 --> 00:19:05,466
All they can be written
as mixed fractions.

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00:19:08,280 --> 00:19:12,753
So let's have a look
at our three halfs.

241
00:19:14,450 --> 00:19:19,078
And what we can do is put two
hearts together to make the

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00:19:19,078 --> 00:19:25,392
whole 1. And we've got 1/2 left
over, so that can be written as

243
00:19:25,392 --> 00:19:26,976
one and a half.

244
00:19:28,040 --> 00:19:32,324
So there are exactly the same,
but written in a different form

245
00:19:32,324 --> 00:19:34,109
1 as a mixed fraction.

246
00:19:34,620 --> 00:19:39,714
And one other top heavy
fraction, an improper fraction

247
00:19:39,714 --> 00:19:44,242
where the numerator is larger
than the denominator.

248
00:19:46,390 --> 00:19:48,202
Let's have a look at another

249
00:19:48,202 --> 00:19:53,906
example. Let's say we
had 8 thirds.

250
00:19:53,910 --> 00:19:55,238
This out the way.

251
00:19:56,780 --> 00:20:00,320
Let's count

252
00:20:00,320 --> 00:20:05,790
out 1234567.
8 thirds

253
00:20:06,900 --> 00:20:11,047
How else can we write that?
How do we write that as a

254
00:20:11,047 --> 00:20:11,685
mixed fraction?

255
00:20:13,110 --> 00:20:16,140
Well, what we're looking
for is how many whole ones

256
00:20:16,140 --> 00:20:17,049
we've got there.

257
00:20:18,310 --> 00:20:22,398
Well, if something's been
divided into 3 pieces.

258
00:20:23,420 --> 00:20:26,150
It takes 3 pieces to make the

259
00:20:26,150 --> 00:20:28,760
whole 1. So that's one whole 1.

260
00:20:30,510 --> 00:20:34,026
There we have another whole 12.

261
00:20:34,890 --> 00:20:42,114
And we've got 2/3 left over,
so 8 thirds is exactly the

262
00:20:42,114 --> 00:20:45,124
same as two and 2/3.

263
00:20:48,770 --> 00:20:50,710
Let's look at one more.

264
00:20:51,710 --> 00:20:55,485
Let's say we had Seven

265
00:20:55,485 --> 00:21:00,999
quarters. Now we know that there
are four quarters in each hole,

266
00:21:00,999 --> 00:21:06,446
one. So we see how many fours go
into Seven. Well, that's one.

267
00:21:06,960 --> 00:21:13,080
And we've got 3 left over, so
we've got one and 3/4.

268
00:21:14,180 --> 00:21:16,784
Let's have a look at one more.

269
00:21:18,090 --> 00:21:21,300
37 tenths

270
00:21:22,920 --> 00:21:27,892
Now we've split something up
into 10 pieces of equal size.

271
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

272
00:21:34,030 --> 00:21:37,030
many 10s, how many whole ones
there are in 37.

273
00:21:38,130 --> 00:21:43,267
Well, three 10s makes 30, so
that's three whole ones, and

274
00:21:43,267 --> 00:21:47,937
we've got 7 leftover, so we've
got 3 and 7/10.

275
00:21:49,020 --> 00:21:52,426
Just move

276
00:21:52,426 --> 00:21:59,202
those. Now let's have
a look at doing the reverse

277
00:21:59,202 --> 00:22:05,676
process. So if we start with a
mixed fraction, how do we turn

278
00:22:05,676 --> 00:22:08,166
it into an improper fraction?

279
00:22:08,740 --> 00:22:11,902
Let's look at three and a

280
00:22:11,902 --> 00:22:16,498
quarter. And if we look at this
visually, we've got.

281
00:22:17,170 --> 00:22:18,658
3 hole once.

282
00:22:20,540 --> 00:22:23,870
And one quarter.

283
00:22:27,500 --> 00:22:29,432
And what we want to turn it

284
00:22:29,432 --> 00:22:33,599
into. Is all
quarters.

285
00:22:34,640 --> 00:22:36,470
So we have a whole 1.

286
00:22:37,360 --> 00:22:43,769
And if we split it into
quarters, we know that a whole 1

287
00:22:43,769 --> 00:22:45,248
needs four quarters.

288
00:22:45,770 --> 00:22:47,280
So we have four there.

289
00:22:47,810 --> 00:22:49,118
Another for their.

290
00:22:49,680 --> 00:22:52,680
Another folder plus this one.

291
00:22:53,310 --> 00:22:56,124
So we've got three force or 12.

292
00:22:56,640 --> 00:23:04,032
Plus the one gives us 13
quarters, so 3 1/4 is exactly

293
00:23:04,032 --> 00:23:07,112
the same as 13 quarters.

294
00:23:07,660 --> 00:23:12,423
Well, let's have a look at how
you might do this.

295
00:23:14,000 --> 00:23:15,500
If you haven't got the visual

296
00:23:15,500 --> 00:23:21,500
aid. Well, what we've actually
got here is our whole number.

297
00:23:22,550 --> 00:23:23,639
And the fraction.

298
00:23:24,240 --> 00:23:25,940
We wanted in quarters.

299
00:23:27,070 --> 00:23:30,686
So what we're doing
is right it again.

300
00:23:31,920 --> 00:23:36,550
We're actually saying We want
four quarters for every hole

301
00:23:36,550 --> 00:23:39,791
one, so we've got three lots of

302
00:23:39,791 --> 00:23:44,910
four. And then what were
ranting on is our one, and

303
00:23:44,910 --> 00:23:46,378
these are all quarters.

304
00:23:47,600 --> 00:23:51,425
So it's the whole number
multiplied by the denominator.

305
00:23:52,460 --> 00:23:56,930
We've added the extra that
we have here. Whatever this

306
00:23:56,930 --> 00:24:01,400
number is, and those are the
number of quarters we've

307
00:24:01,400 --> 00:24:07,211
got. So we've got our 3/4 of
12 + 1/4, so 13 quarters.

308
00:24:08,940 --> 00:24:10,956
Let's have a look at one more

309
00:24:10,956 --> 00:24:16,478
example. Let's say we've got
five and two ninths.

310
00:24:18,310 --> 00:24:21,086
We want to turn it
into this format.

311
00:24:22,360 --> 00:24:28,632
Ninths well, if we want to take
a whole one, we wouldn't need 9

312
00:24:28,632 --> 00:24:34,904
ninths and we've got five whole
ones, so we're going to have 5 *

313
00:24:34,904 --> 00:24:37,592
9 lots of 9th this time.

314
00:24:38,250 --> 00:24:42,660
And then we need to add on the
two nights that we have here.

315
00:24:42,670 --> 00:24:50,530
So 5 nines of 45 plus
the two and that all 9th.

316
00:24:50,530 --> 00:24:53,805
So we have 47 ninths.

317
00:24:57,170 --> 00:25:00,734
Any whole number can be written
as a fraction.

318
00:25:01,270 --> 00:25:04,078
So for example, if we take
the number 2.

319
00:25:05,930 --> 00:25:10,097
If we write it with the
denominator of one.

320
00:25:11,580 --> 00:25:13,860
We've written it as a fraction.

321
00:25:15,050 --> 00:25:20,143
And any equivalent form, so we
could have 4 over 2.

322
00:25:20,770 --> 00:25:24,370
30 over

323
00:25:24,370 --> 00:25:31,193
15. And so on.
So any whole number can be

324
00:25:31,193 --> 00:25:35,963
written as a fraction with a
numerator and a denominator.

325
00:25:37,560 --> 00:25:45,186
So fractions.
They can appear in a number

326
00:25:45,186 --> 00:25:50,460
of different forms. You might
see proper fractions, improper

327
00:25:50,460 --> 00:25:52,218
fractions, mixed fractions.

328
00:25:53,060 --> 00:25:57,272
And you can see lots of
different equivalent fractions.

329
00:25:57,870 --> 00:26:00,255
So that all different
ways that we see them.