WEBVTT

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We're now going to have a look
at adding and subtracting

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fractions. Let's start
with 1/5 +

00:00:12.140 --> 00:00:16.094
2/5. Here I

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have 1/5. And
here 2/5.

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If we add them together.

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We have 3/5.

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So what I've done is added the
numerators of the two fractions.

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So 1 + 2 gives me 3/5.

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Let's have a look
at another example.

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Let's say we have 1/8
another one 8th.

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And. 5/8
So in the same way.

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I have 1/8.

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Another rates, so that's 2

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eighths. And then 5 eights
to add on. So that gives me

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a total of 7/8.

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If we're adding like fractions,
so the fractions are all of the

00:01:19.548 --> 00:01:25.587
same size. Here we had eighths,
so all the denominators were

00:01:25.587 --> 00:01:29.098
eight. We can just
add the numerators.

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Here the denominators were
fifths. They were the same size,

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so we could add the numerators.

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Subtraction is very similar.

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Let's have 5/8.

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And this time will take
away 3/8.

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The denominators are the same,
so we have the same type of

00:01:55.256 --> 00:02:01.721
fraction. So we can just do
five takeaway. Three gives us 2

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eighths. And if we put that into
its lowest form.

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That's one quarter.

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Let's have a look at another
addition one now, this time

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let's have 3/5 + 4/5.

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And when we add them three
at 4 gives us 7 fifths.

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So we've added two proper
fractions and they've added

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together to give an improper
fraction of fraction that's

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larger than one. And if we write
it as a mixed fraction, 5 goes

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into Seven, once with two left
over. So that's exactly the same

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as one and 2/5.

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OK, let's look now at what
happens when we have fractions

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where the denominators are not

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the same. Let's say
we have 1/2

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+ 1/4. So let's have

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a look. We have 1/2.

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Plus 1/4.

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We can add them together.

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But what do we end up with? How
can we describe the fraction

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that we have?

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Well, we know that 1/2.

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Is the same.

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That's two quarters.

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So if we change our half, we
find an equivalent fraction of

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two quarters and then add our
quarter. We are now in the

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situation where the denominators
are the same.

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So we can simply add the
numerators so we get 3/4.

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Let's have
a look

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at 3/4

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+ 3/8. The
denominators are not the same.

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So imagine now we have 3/4.

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And we have 3/8.

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What we need to do?

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Is to make these.

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Into eighths. Go back
looking visually again.

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Those are three quarters.

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Nicer

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3/8.

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Well.
In fact, visually we

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can see an answer.

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Straight away. We've got a whole
one here and one 8th.

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But let's actually see.

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What is happening numerically
here? We can't turn eighths into

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the quarters very easily if
we've got two of them. Yes,

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that's a quarter. But we've got
this one left over.

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But what we can do is turn our

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quarters. Into eighths
because 2 eighths fit very

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nicely into a quarter.

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So what we have instead of 3/4
is 2 eighths there, 2 eighth

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there and two eighths there.

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So we have 6 eighths.

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Plus Are

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3/8. Now again.

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We have fractions with the same
denominators, so we can just add

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the numerators, so we get 9
eighths which we saw at the

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beginning. Is a whole 1.

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With one 8th leftover.

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Now here we've used fractions
where they're in the same sort

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of family because 8th fitted
exactly into quarters.

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Quarters fit exactly into halfs.

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What happens when it's not quite

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so convenient? Well, let's have

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a look. At
1/2 + 1/3.

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So what we wanted to add

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together is 1/2. Plus the third.

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Now if we tried to turn the half
into thirds, we'd have

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difficulty 'cause it doesn't fit
a whole number of times.

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So what we need to find?

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Is a fraction of the

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denominator. That fits into

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thirds. As well as into half.

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And in this case.

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That fraction is
6.

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We can fit 26 into our third
and a half.

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Is 36.

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So we're finding an
equivalent fraction for half

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is 36. And
a third is 26.

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So again, with the denominators
now the same.

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We can just add the numerators
and we see we've got a total of

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5, six, 3 + 2 giving us 5.

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Let's try another one now.

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Let's look
at 1/4

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+ 2/5.

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Now. We
need to find a number

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for our denominator.

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That for is going to fit into so
it can be divided.

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Into quarters, and that five is
going to fit into.

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Well, let's have a look at some
numbers that four and five fit

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into. Let's start with full.

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Well, two Forza 8.

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Three Forza 12. So
these are all numbers

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multiples of four sixteen

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2024. And so on.

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And let's have a look at numbers
that 5 fit into was 510.

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15

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20 Ha, I
can stop there because I've now

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found a common number of one
that's in both.

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The force on the fives

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so 20. Is a

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common denominator. So we're
going to change our quarters.

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Into Twentieths.

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Well, how many?

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Did we need 12345? So five
20th is the same as a

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quarter? And 2/5.

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Well, we need it.

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1234

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20th make one face, but
we've got 2/5 so we've

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got eight twentieths.

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So in total now we've got the
denominate are the same.

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Eight at 5 gives
us 13 twentieths.

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Let's have a look at this
now numerically. We've done it

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by. Thinking about it by perhaps
visualizing it in our heads,

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let's have a look at numerically
what's actually happening.

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There's 1/4

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+ 2/5.
How did we arrive

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at this 20?

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Well, we were looking for a
number that both four and five

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fitted into a common number.

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So what you could say we did
here is actually multiplied. The

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four and the five.

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4. Goes into 25 times.
So what we did is

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multiplied 4 by 5.

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Now. With our fractions,
whatever we've done to the

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denominator to find an
equivalent fraction, we must do

00:11:11.542 --> 00:11:13.072
the same to the numerator.

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So we had to multiply this one
by five also.

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Our 2/5.

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We multiplied the five by four
to make 20.

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Whatever we multiply the
denominator by, we must multiply

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the numerator by and our
numerator was too.

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So we have to do 2 * 4.

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And this is how we arrived at
our five 20th 155.

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4 fives are 20.

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2408

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So that's a plus, and five
fours or 20, giving us a

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total of 13 twentieths.

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Let's have a
look at Subtraction.

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This time, let's
have 3/4 takeaway.

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16 So again, we're
looking for numbers that both

00:12:25.054 --> 00:12:28.219
four and six fit into.

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Let's have a look
at our force 48.

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1216
2024 and so

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on. And
our sixes multiples

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of six 612-1824.

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And so on.

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The reason I've written so many
is that I want to point out to

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you that there.

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Might be more than one common

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pair. 12 is a common
denominator, both four and six

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fit into 12.

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But also there's another one

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here 24. And those four and six.

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Fit into 24 and in fact if we
multiply 4 and six together we

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get 24. But as you can see in
this case that's not the lowest

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common denominator. It's not the
lowest number that is common to

00:13:37.175 --> 00:13:38.795
both of these denominators.

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We want to use the lowest one
'cause if we don't we then need

00:13:45.130 --> 00:13:48.650
the end of the calculation to
actually reduce the fraction to

00:13:48.650 --> 00:13:52.170
its lowest form, and it's much
easier to deal with smaller

00:13:52.170 --> 00:13:54.410
numbers. So we try and find the

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lowest one. So we want to write
for. We want to turn it into an

00:14:01.674 --> 00:14:04.422
equivalent fraction with 12 as a

00:14:04.422 --> 00:14:09.488
denominator. So what have we
done to fall to make it 12?

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We've multiplied by three, so we
must multiply the numerator by

00:14:14.086 --> 00:14:19.515
three. What have we done to our
six to make it 12?

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We've multiplied by two.

00:14:23.240 --> 00:14:28.088
So we must multiply our
numerator by two.

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33943 twelve takeaway. Once too
is 26 twos at 12, now

00:14:35.031 --> 00:14:41.972
are denominators are the same,
so we can simply subtract the

00:14:41.972 --> 00:14:47.020
numerators, giving us a result
of Seven twelfths.

00:14:49.230 --> 00:14:54.100
So what we're doing when we add
and subtract fractions?

00:14:55.580 --> 00:15:01.436
Is we need to make sure that
the denominators are the same

00:15:01.436 --> 00:15:06.316
before we do the addition of
the subtraction. If they're

00:15:06.316 --> 00:15:11.684
not the same, then we need to
find the lowest common

00:15:11.684 --> 00:15:15.100
denominator between the
fractions and then find

00:15:15.100 --> 00:15:19.492
equivalent fractions, and then
we can do the additional

00:15:19.492 --> 00:15:19.980
subtraction.

00:15:21.950 --> 00:15:27.709
What we need to look at now is
when we have mixed fractions.

00:15:28.350 --> 00:15:33.634
Let's say
we've got

00:15:33.634 --> 00:15:37.597
5 and 3/4.

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And we're going to take away one
and four fifths. How do we deal

00:15:45.694 --> 00:15:48.100
with that? Well.

00:15:48.600 --> 00:15:53.122
The first thing that we need to
do is to turn them into improper

00:15:53.122 --> 00:15:58.063
fractions. We need to make them
so that they're all over, in

00:15:58.063 --> 00:16:00.887
this case quarters, and with
this one, fifths.

00:16:01.490 --> 00:16:05.798
Then we can do the process that
we've just done finding common

00:16:05.798 --> 00:16:07.234
denominators and actually doing

00:16:07.234 --> 00:16:12.280
the Subtraction. So first of
all, we need to find out how

00:16:12.280 --> 00:16:16.416
many quarters we have here.
Well, we've got five whole ones

00:16:16.416 --> 00:16:20.928
we want to make them into
quarters. So we multiplied by 4.

00:16:22.040 --> 00:16:25.563
And then we're going to add the
sorry that we've got there. So

00:16:25.563 --> 00:16:26.918
that's how many quarters we

00:16:26.918 --> 00:16:30.190
have. I'm going to take away.

00:16:31.440 --> 00:16:33.288
One and four fifths.

00:16:33.980 --> 00:16:40.754
So. 1 * 5 that's how
many fifths are in a whole one

00:16:40.754 --> 00:16:42.125
plus the four.

00:16:42.880 --> 00:16:44.932
And that's how many fifths we

00:16:44.932 --> 00:16:51.860
have. 4 fives are 20
+ 3 is 20 three quarters.

00:16:52.480 --> 00:16:58.600
Take away once five is 5 plus,
the four is 9 fifths.

00:16:59.470 --> 00:17:01.840
Now we need to find.

00:17:02.390 --> 00:17:04.875
The common denominator of four

00:17:04.875 --> 00:17:10.474
and five. Well, as we
found before, that's 20.

00:17:10.980 --> 00:17:18.134
What have we multiplied 4 by to
make 20 that's five, so we have

00:17:18.134 --> 00:17:20.689
to have 23 * 5.

00:17:21.460 --> 00:17:28.181
Take away 20th. What do we
multiply 5 by to get 20? Well

00:17:28.181 --> 00:17:31.800
that was four so 9 * 4.

00:17:32.520 --> 00:17:35.340
So 23 * 5.

00:17:36.060 --> 00:17:42.812
Five 20s or 100
three 5:15 so it's

00:17:42.812 --> 00:17:48.720
115 twentieths takeaway for
9:30 six 20th.

00:17:49.500 --> 00:17:52.149
Now I denominators.

00:17:52.650 --> 00:17:57.780
Are the same. We can simply
subtract the numerators.

00:17:58.480 --> 00:18:05.662
115 takeaway 36 is 79 so we
have 70 nine 20th and usually if

00:18:05.662 --> 00:18:11.818
our question is given in terms
of a mixed fraction then we

00:18:11.818 --> 00:18:15.409
ought to give our answer in the

00:18:15.409 --> 00:18:22.930
same form. So 20s into
79 or twenty 20th make one

00:18:22.930 --> 00:18:28.910
whole 1. And we've got three
whole ones there. Three 20s are

00:18:28.910 --> 00:18:35.962
60. And then we've got
19 twentieths leftover. So the

00:18:35.962 --> 00:18:39.850
answer is 3 and 19 twentieths.

00:18:40.670 --> 00:18:44.774
Let's have a look at one
more example.

00:18:45.850 --> 00:18:52.222
This time using three fractions,
so one and 3/4.

00:18:53.050 --> 00:18:56.590
Plus 6 and 2/5.

00:18:58.320 --> 00:19:02.310
+5 halfs so we've got a mixture

00:19:02.310 --> 00:19:06.280
here. Of mixed fractions and an

00:19:06.280 --> 00:19:10.924
improper fraction. Well, as
before, the first thing we need

00:19:10.924 --> 00:19:14.642
to do is to turn these mixed
fractions into improper ones.

00:19:15.380 --> 00:19:19.238
Here we have one whole 1.

00:19:20.310 --> 00:19:26.610
We need to turn it into quarters
so we multiply by 4 and we add

00:19:26.610 --> 00:19:29.970
the three. That's how many
quarters we have.

00:19:30.680 --> 00:19:36.400
And then we add six whole ones.
We turn them into fifths, we

00:19:36.400 --> 00:19:37.720
multiply by 5.

00:19:38.380 --> 00:19:44.060
We add the two not so
many fests we have

00:19:44.060 --> 00:19:46.332
plus our five halves.

00:19:47.530 --> 00:19:54.640
Once for is 4 +
3 is 7 quarters plus

00:19:54.640 --> 00:20:01.039
six 530 + 2. Thirty
2/5 + 5 halfs.

00:20:02.490 --> 00:20:07.722
Now this time we need to find
common denominator of all three

00:20:07.722 --> 00:20:09.030
of these denominators.

00:20:09.890 --> 00:20:16.162
Now it's easier to think perhaps
of the largest 1 first, so if I

00:20:16.162 --> 00:20:18.850
think and count up, perhaps in

00:20:18.850 --> 00:20:24.284
fives. 5 obviously is not common
to these two 10. Well two goes

00:20:24.284 --> 00:20:26.366
into 10, but the four doesn't.

00:20:26.910 --> 00:20:31.167
So let's keep going 15. That's
no good 20.

00:20:31.690 --> 00:20:36.548
Yep, five goes into 20. Two were
going to 20 and so will fall.

00:20:37.100 --> 00:20:42.482
So 20 is going to be
my common denominator.

00:20:42.590 --> 00:20:45.218
So it's just right. All the

00:20:45.218 --> 00:20:47.970
denominators in. So what did I

00:20:47.970 --> 00:20:54.239
do to fall? To get 20
I multiplied by 5.

00:20:55.110 --> 00:20:57.714
So 7 must be multiplied by 5.

00:20:58.890 --> 00:21:06.426
What did I do to five to get
20? I multiplied by 4, so I must

00:21:06.426 --> 00:21:12.078
do 32 * 4. The numerator and the
denominator must be multiplied

00:21:12.078 --> 00:21:13.962
by the same number.

00:21:13.970 --> 00:21:19.724
And finally, what did I do to
the two to get the 20? I

00:21:19.724 --> 00:21:24.245
multiplied by 10, so I must
multiply the numerator by 10.

00:21:24.860 --> 00:21:28.276
7 fives gives us

00:21:28.276 --> 00:21:36.064
35. Plus 430 twos
for 30s or 122, Forza

00:21:36.064 --> 00:21:42.448
8 says 120, eight, 20th
plus 50 twentieths.

00:21:43.540 --> 00:21:45.580
And if we add these altogether.

00:21:46.470 --> 00:21:50.222
We get 100 and

00:21:50.222 --> 00:21:51.160
28178.

00:21:52.140 --> 00:21:57.380
213
20th.

00:21:59.090 --> 00:22:04.022
And again, let's turn that back
to a mixed fraction. How many

00:22:04.022 --> 00:22:07.721
20s? How many whole ones are
there in 213?

00:22:08.270 --> 00:22:15.602
Well, 20 * 10 gets us
to 200, so that's ten whole

00:22:15.602 --> 00:22:18.657
ones and 13 twentieths leftover.

00:22:19.200 --> 00:22:24.764
So if we add one and three
quarters 6 and 2/5 and five

00:22:24.764 --> 00:22:27.760
halfs, we get 10 and 13
twentieths.