• 0:01 - 0:05
We're now going to have a look
• 0:05 - 0:12
fractions. Let's start
with 1/5 +
• 0:12 - 0:16
2/5. Here I
• 0:16 - 0:21
have 1/5. And
here 2/5.
• 0:22 - 0:24
• 0:25 - 0:29
We have 3/5.
• 0:29 - 0:35
So what I've done is added the
numerators of the two fractions.
• 0:35 - 0:38
So 1 + 2 gives me 3/5.
• 0:39 - 0:44
Let's have a look
at another example.
• 0:45 - 0:51
Let's say we have 1/8
another one 8th.
• 0:52 - 1:00
And. 5/8
So in the same way.
• 1:01 - 1:02
I have 1/8.
• 1:03 - 1:05
Another rates, so that's 2
• 1:05 - 1:10
eighths. And then 5 eights
to add on. So that gives me
• 1:10 - 1:12
a total of 7/8.
• 1:13 - 1:20
so the fractions are all of the
• 1:20 - 1:26
same size. Here we had eighths,
so all the denominators were
• 1:26 - 1:29
eight. We can just
• 1:30 - 1:34
Here the denominators were
fifths. They were the same size,
• 1:34 - 1:37
so we could add the numerators.
• 1:39 - 1:41
Subtraction is very similar.
• 1:41 - 1:44
Let's have 5/8.
• 1:45 - 1:49
And this time will take
away 3/8.
• 1:51 - 1:55
The denominators are the same,
so we have the same type of
• 1:55 - 2:02
fraction. So we can just do
five takeaway. Three gives us 2
• 2:02 - 2:07
eighths. And if we put that into
its lowest form.
• 2:07 - 2:08
That's one quarter.
• 2:10 - 2:16
Let's have a look at another
• 2:16 - 2:19
let's have 3/5 + 4/5.
• 2:20 - 2:27
And when we add them three
at 4 gives us 7 fifths.
• 2:28 - 2:32
• 2:32 - 2:36
together to give an improper
fraction of fraction that's
• 2:36 - 2:42
larger than one. And if we write
it as a mixed fraction, 5 goes
• 2:42 - 2:47
into Seven, once with two left
over. So that's exactly the same
• 2:47 - 2:49
as one and 2/5.
• 2:50 - 2:56
OK, let's look now at what
happens when we have fractions
• 2:56 - 2:59
where the denominators are not
• 2:59 - 3:06
the same. Let's say
we have 1/2
• 3:06 - 3:10
+ 1/4. So let's have
• 3:10 - 3:14
a look. We have 1/2.
• 3:14 - 3:16
Plus 1/4.
• 3:17 - 3:19
• 3:19 - 3:25
But what do we end up with? How
can we describe the fraction
• 3:25 - 3:26
that we have?
• 3:27 - 3:30
Well, we know that 1/2.
• 3:30 - 3:32
Is the same.
• 3:32 - 3:36
That's two quarters.
• 3:36 - 3:42
So if we change our half, we
find an equivalent fraction of
• 3:42 - 3:48
two quarters and then add our
quarter. We are now in the
• 3:48 - 3:51
situation where the denominators
are the same.
• 3:52 - 3:58
So we can simply add the
numerators so we get 3/4.
• 3:58 - 4:05
Let's have
a look
• 4:05 - 4:08
at 3/4
• 4:08 - 4:15
+ 3/8. The
denominators are not the same.
• 4:16 - 4:19
So imagine now we have 3/4.
• 4:21 - 4:23
And we have 3/8.
• 4:24 - 4:26
What we need to do?
• 4:26 - 4:28
Is to make these.
• 4:29 - 4:34
Into eighths. Go back
looking visually again.
• 4:37 - 4:39
Those are three quarters.
• 4:40 - 4:43
Nicer
• 4:43 - 4:46
3/8.
• 4:46 - 4:51
Well.
In fact, visually we
• 4:51 - 4:53
• 4:54 - 4:59
Straight away. We've got a whole
one here and one 8th.
• 5:00 - 5:01
But let's actually see.
• 5:02 - 5:06
What is happening numerically
here? We can't turn eighths into
• 5:06 - 5:11
the quarters very easily if
we've got two of them. Yes,
• 5:11 - 5:15
that's a quarter. But we've got
this one left over.
• 5:15 - 5:19
But what we can do is turn our
• 5:19 - 5:23
quarters. Into eighths
because 2 eighths fit very
• 5:23 - 5:25
nicely into a quarter.
• 5:27 - 5:33
So what we have instead of 3/4
is 2 eighths there, 2 eighth
• 5:33 - 5:35
there and two eighths there.
• 5:36 - 5:39
So we have 6 eighths.
• 5:40 - 5:42
Plus Are
• 5:42 - 5:45
3/8. Now again.
• 5:46 - 5:51
We have fractions with the same
denominators, so we can just add
• 5:51 - 5:56
the numerators, so we get 9
eighths which we saw at the
• 5:56 - 5:58
beginning. Is a whole 1.
• 5:58 - 6:00
With one 8th leftover.
• 6:01 - 6:08
Now here we've used fractions
where they're in the same sort
• 6:08 - 6:13
of family because 8th fitted
exactly into quarters.
• 6:14 - 6:17
Quarters fit exactly into halfs.
• 6:17 - 6:20
What happens when it's not quite
• 6:20 - 6:23
so convenient? Well, let's have
• 6:23 - 6:29
a look. At
1/2 + 1/3.
• 6:30 - 6:32
So what we wanted to add
• 6:32 - 6:35
together is 1/2. Plus the third.
• 6:37 - 6:41
Now if we tried to turn the half
into thirds, we'd have
• 6:41 - 6:45
difficulty 'cause it doesn't fit
a whole number of times.
• 6:46 - 6:48
So what we need to find?
• 6:49 - 6:51
Is a fraction of the
• 6:51 - 6:54
denominator. That fits into
• 6:54 - 6:57
thirds. As well as into half.
• 6:58 - 7:00
And in this case.
• 7:00 - 7:05
That fraction is
6.
• 7:07 - 7:12
We can fit 26 into our third
and a half.
• 7:13 - 7:16
Is 36.
• 7:17 - 7:24
So we're finding an
equivalent fraction for half
• 7:24 - 7:31
is 36. And
a third is 26.
• 7:31 - 7:34
So again, with the denominators
now the same.
• 7:35 - 7:42
We can just add the numerators
and we see we've got a total of
• 7:42 - 7:45
5, six, 3 + 2 giving us 5.
• 7:46 - 7:49
Let's try another one now.
• 7:52 - 7:58
Let's look
at 1/4
• 7:58 - 8:00
+ 2/5.
• 8:01 - 8:08
Now. We
need to find a number
• 8:08 - 8:09
for our denominator.
• 8:10 - 8:14
That for is going to fit into so
it can be divided.
• 8:15 - 8:18
Into quarters, and that five is
going to fit into.
• 8:19 - 8:23
Well, let's have a look at some
numbers that four and five fit
• 8:23 - 8:26
• 8:26 - 8:30
Well, two Forza 8.
• 8:30 - 8:36
Three Forza 12. So
these are all numbers
• 8:36 - 8:40
multiples of four sixteen
• 8:40 - 8:42
2024. And so on.
• 8:44 - 8:51
And let's have a look at numbers
that 5 fit into was 510.
• 8:52 - 8:53
15
• 8:54 - 9:01
20 Ha, I
can stop there because I've now
• 9:01 - 9:06
found a common number of one
that's in both.
• 9:06 - 9:10
The force on the fives
• 9:10 - 9:14
so 20. Is a
• 9:14 - 9:20
common denominator. So we're
going to change our quarters.
• 9:20 - 9:22
Into Twentieths.
• 9:23 - 9:26
Well, how many?
• 9:27 - 9:35
Did we need 12345? So five
20th is the same as a
• 9:35 - 9:38
quarter? And 2/5.
• 9:40 - 9:42
Well, we need it.
• 9:42 - 9:47
1234
• 9:49 - 9:55
20th make one face, but
we've got 2/5 so we've
• 9:55 - 9:56
got eight twentieths.
• 9:58 - 10:02
So in total now we've got the
denominate are the same.
• 10:03 - 10:08
Eight at 5 gives
us 13 twentieths.
• 10:09 - 10:15
Let's have a look at this
now numerically. We've done it
• 10:15 - 10:20
by. Thinking about it by perhaps
• 10:20 - 10:23
let's have a look at numerically
what's actually happening.
• 10:24 - 10:27
There's 1/4
• 10:27 - 10:34
+ 2/5.
How did we arrive
• 10:34 - 10:36
at this 20?
• 10:38 - 10:42
Well, we were looking for a
number that both four and five
• 10:42 - 10:44
fitted into a common number.
• 10:47 - 10:51
So what you could say we did
here is actually multiplied. The
• 10:51 - 10:53
four and the five.
• 10:55 - 11:02
4. Goes into 25 times.
So what we did is
• 11:02 - 11:04
multiplied 4 by 5.
• 11:05 - 11:09
Now. With our fractions,
whatever we've done to the
• 11:09 - 11:12
denominator to find an
equivalent fraction, we must do
• 11:12 - 11:13
the same to the numerator.
• 11:14 - 11:18
So we had to multiply this one
by five also.
• 11:20 - 11:22
Our 2/5.
• 11:23 - 11:28
We multiplied the five by four
to make 20.
• 11:29 - 11:34
Whatever we multiply the
denominator by, we must multiply
• 11:34 - 11:38
the numerator by and our
numerator was too.
• 11:38 - 11:41
So we have to do 2 * 4.
• 11:42 - 11:46
And this is how we arrived at
our five 20th 155.
• 11:47 - 11:48
4 fives are 20.
• 11:49 - 11:51
2408
• 11:53 - 12:00
So that's a plus, and five
fours or 20, giving us a
• 12:00 - 12:02
total of 13 twentieths.
• 12:04 - 12:11
Let's have a
look at Subtraction.
• 12:12 - 12:18
This time, let's
have 3/4 takeaway.
• 12:18 - 12:25
16 So again, we're
looking for numbers that both
• 12:25 - 12:28
four and six fit into.
• 12:29 - 12:36
Let's have a look
at our force 48.
• 12:36 - 12:43
1216
2024 and so
• 12:43 - 12:50
on. And
our sixes multiples
• 12:50 - 12:54
of six 612-1824.
• 12:54 - 12:56
And so on.
• 12:57 - 13:03
The reason I've written so many
is that I want to point out to
• 13:03 - 13:04
you that there.
• 13:04 - 13:07
Might be more than one common
• 13:07 - 13:13
pair. 12 is a common
denominator, both four and six
• 13:13 - 13:15
fit into 12.
• 13:15 - 13:17
But also there's another one
• 13:17 - 13:21
here 24. And those four and six.
• 13:21 - 13:27
Fit into 24 and in fact if we
multiply 4 and six together we
• 13:27 - 13:33
get 24. But as you can see in
this case that's not the lowest
• 13:33 - 13:37
common denominator. It's not the
lowest number that is common to
• 13:37 - 13:39
both of these denominators.
• 13:41 - 13:45
We want to use the lowest one
'cause if we don't we then need
• 13:45 - 13:49
the end of the calculation to
actually reduce the fraction to
• 13:49 - 13:52
its lowest form, and it's much
easier to deal with smaller
• 13:52 - 13:54
numbers. So we try and find the
• 13:54 - 14:02
lowest one. So we want to write
for. We want to turn it into an
• 14:02 - 14:04
equivalent fraction with 12 as a
• 14:04 - 14:09
denominator. So what have we
done to fall to make it 12?
• 14:09 - 14:14
We've multiplied by three, so we
must multiply the numerator by
• 14:14 - 14:20
three. What have we done to our
six to make it 12?
• 14:21 - 14:22
We've multiplied by two.
• 14:23 - 14:28
So we must multiply our
numerator by two.
• 14:28 - 14:35
33943 twelve takeaway. Once too
is 26 twos at 12, now
• 14:35 - 14:42
are denominators are the same,
so we can simply subtract the
• 14:42 - 14:47
numerators, giving us a result
of Seven twelfths.
• 14:49 - 14:54
So what we're doing when we add
and subtract fractions?
• 14:56 - 15:01
Is we need to make sure that
the denominators are the same
• 15:01 - 15:06
before we do the addition of
the subtraction. If they're
• 15:06 - 15:12
not the same, then we need to
find the lowest common
• 15:12 - 15:15
denominator between the
fractions and then find
• 15:15 - 15:19
equivalent fractions, and then
• 15:19 - 15:20
subtraction.
• 15:22 - 15:28
What we need to look at now is
when we have mixed fractions.
• 15:28 - 15:34
Let's say
we've got
• 15:34 - 15:38
5 and 3/4.
• 15:39 - 15:46
And we're going to take away one
and four fifths. How do we deal
• 15:46 - 15:48
with that? Well.
• 15:49 - 15:53
The first thing that we need to
do is to turn them into improper
• 15:53 - 15:58
fractions. We need to make them
so that they're all over, in
• 15:58 - 16:01
this case quarters, and with
this one, fifths.
• 16:01 - 16:06
Then we can do the process that
we've just done finding common
• 16:06 - 16:07
denominators and actually doing
• 16:07 - 16:12
the Subtraction. So first of
all, we need to find out how
• 16:12 - 16:16
many quarters we have here.
Well, we've got five whole ones
• 16:16 - 16:21
we want to make them into
quarters. So we multiplied by 4.
• 16:22 - 16:26
And then we're going to add the
sorry that we've got there. So
• 16:26 - 16:27
that's how many quarters we
• 16:27 - 16:30
have. I'm going to take away.
• 16:31 - 16:33
One and four fifths.
• 16:34 - 16:41
So. 1 * 5 that's how
many fifths are in a whole one
• 16:41 - 16:42
plus the four.
• 16:43 - 16:45
And that's how many fifths we
• 16:45 - 16:52
have. 4 fives are 20
+ 3 is 20 three quarters.
• 16:52 - 16:59
Take away once five is 5 plus,
the four is 9 fifths.
• 16:59 - 17:02
Now we need to find.
• 17:02 - 17:05
The common denominator of four
• 17:05 - 17:10
and five. Well, as we
found before, that's 20.
• 17:11 - 17:18
What have we multiplied 4 by to
make 20 that's five, so we have
• 17:18 - 17:21
to have 23 * 5.
• 17:21 - 17:28
Take away 20th. What do we
multiply 5 by to get 20? Well
• 17:28 - 17:32
that was four so 9 * 4.
• 17:33 - 17:35
So 23 * 5.
• 17:36 - 17:43
Five 20s or 100
three 5:15 so it's
• 17:43 - 17:49
115 twentieths takeaway for
9:30 six 20th.
• 17:50 - 17:52
Now I denominators.
• 17:53 - 17:58
Are the same. We can simply
subtract the numerators.
• 17:58 - 18:06
115 takeaway 36 is 79 so we
have 70 nine 20th and usually if
• 18:06 - 18:12
our question is given in terms
of a mixed fraction then we
• 18:12 - 18:15
ought to give our answer in the
• 18:15 - 18:23
same form. So 20s into
79 or twenty 20th make one
• 18:23 - 18:29
whole 1. And we've got three
whole ones there. Three 20s are
• 18:29 - 18:36
60. And then we've got
19 twentieths leftover. So the
• 18:36 - 18:40
answer is 3 and 19 twentieths.
• 18:41 - 18:45
Let's have a look at one
more example.
• 18:46 - 18:52
This time using three fractions,
so one and 3/4.
• 18:53 - 18:57
Plus 6 and 2/5.
• 18:58 - 19:02
+5 halfs so we've got a mixture
• 19:02 - 19:06
here. Of mixed fractions and an
• 19:06 - 19:11
improper fraction. Well, as
before, the first thing we need
• 19:11 - 19:15
to do is to turn these mixed
fractions into improper ones.
• 19:15 - 19:19
Here we have one whole 1.
• 19:20 - 19:27
We need to turn it into quarters
so we multiply by 4 and we add
• 19:27 - 19:30
the three. That's how many
quarters we have.
• 19:31 - 19:36
And then we add six whole ones.
We turn them into fifths, we
• 19:36 - 19:38
multiply by 5.
• 19:38 - 19:44
We add the two not so
many fests we have
• 19:44 - 19:46
plus our five halves.
• 19:48 - 19:55
Once for is 4 +
3 is 7 quarters plus
• 19:55 - 20:01
six 530 + 2. Thirty
2/5 + 5 halfs.
• 20:02 - 20:08
Now this time we need to find
common denominator of all three
• 20:08 - 20:09
of these denominators.
• 20:10 - 20:16
Now it's easier to think perhaps
of the largest 1 first, so if I
• 20:16 - 20:19
think and count up, perhaps in
• 20:19 - 20:24
fives. 5 obviously is not common
to these two 10. Well two goes
• 20:24 - 20:26
into 10, but the four doesn't.
• 20:27 - 20:31
So let's keep going 15. That's
no good 20.
• 20:32 - 20:37
Yep, five goes into 20. Two were
going to 20 and so will fall.
• 20:37 - 20:42
So 20 is going to be
my common denominator.
• 20:43 - 20:45
So it's just right. All the
• 20:45 - 20:48
denominators in. So what did I
• 20:48 - 20:54
do to fall? To get 20
I multiplied by 5.
• 20:55 - 20:58
So 7 must be multiplied by 5.
• 20:59 - 21:06
What did I do to five to get
20? I multiplied by 4, so I must
• 21:06 - 21:12
do 32 * 4. The numerator and the
denominator must be multiplied
• 21:12 - 21:14
by the same number.
• 21:14 - 21:20
And finally, what did I do to
the two to get the 20? I
• 21:20 - 21:24
multiplied by 10, so I must
multiply the numerator by 10.
• 21:25 - 21:28
7 fives gives us
• 21:28 - 21:36
35. Plus 430 twos
for 30s or 122, Forza
• 21:36 - 21:42
8 says 120, eight, 20th
plus 50 twentieths.
• 21:44 - 21:46
And if we add these altogether.
• 21:46 - 21:50
We get 100 and
• 21:50 - 21:51
28178.
• 21:52 - 21:57
213
20th.
• 21:59 - 22:04
And again, let's turn that back
to a mixed fraction. How many
• 22:04 - 22:08
20s? How many whole ones are
there in 213?
• 22:08 - 22:16
Well, 20 * 10 gets us
to 200, so that's ten whole
• 22:16 - 22:19
ones and 13 twentieths leftover.
• 22:19 - 22:25
So if we add one and three
quarters 6 and 2/5 and five
• 22:25 - 22:28
halfs, we get 10 and 13
twentieths.
Title: