Adding and Subtracting Mixed fractions Video Lecture - Class 6

hello friends this video on fractions
part 18 is brought to you by exam viacom
no more fear from exam so now that we
have discussed both lies and unlike
fractions how do you think we add mixed
fractions so we have already discussed
about mixed fractions right two mixed
fractions have something very
interesting they have to hold them apart
as well as the fractional part something
like to 3 by 4 1 1 by 3 so these are all
mixed fractions now if you have to add
to such mixed fractions so how do you
add them because in that case just by
looking at them you will not know if
they are like fractions if there are
like fractions even in there like
fractions you do not have just one
denominator you also have the whole
number part so how do you handle all of
that so let us look at an example now
there are two different methods of doing
mixed fraction now we will discuss the
first method method one so in method 1
what we do is whatever mixed fractions
are given in the problem we just convert
them in the form of improper fractions
because by now we all know that mixed
fractions are nothing but they are
improper fractions which are expressed
in a way such that tails a separate
whole number part and there is a
separate fraction but otherwise they are
improper fractions only so let us take
an example so the first example we take
2 3 by 4 plus 1 1 by 4 let's say that
you have to add these two mixed
fractions so what you do you convert
this into improper fraction how you
convert into improper fraction remember
mix to improper you have to remember mad
first multiply then add so you go like
this multiply then add so go to say 8 8
plus 3 11 so this is 11 by 4 what is
this
4 into 1 4 plus 1 that is 5 by 4 so it
is 11 by 4 plus 5 by 4 so these are like
fractions again same denominator so you
just need to add the numerators so this
is 16 by 4 so this would be the answer
let's take another example where we deal
with an
fractions for example you have to add to
3 by 4 with 1 1 by 5 so now you have
different denominators right so they're
unlike but still let us convert them
into improper fractions first so 4 into
2 is 8 plus 3 is 11 so 11 by 4 plus 5
into 1 is 5 plus 1 6 so 6 by 5 so in
this case what you what would be your
next step
so next step we will find out LCM of 4 &
5 which is 20 now once we have found out
the LCM our job is to convert each of
these fractions into equivalent
fractions so we have to convert 11 by 4
into a form such that the denominator is
20 so for that we multiply the numerator
and denominator by 5 so you get 55 by 24
the second key is 6 by 5 again multiply
the numerator and denominator by 4 so
that will give 24 by 20 so now 11 by 4
can be written as 55 by 20 and 6 by 5
can be written as 24 by 20 so this
becomes 55 plus 24 divided by 20 so 55
plus 24 is 79 by 20 so 79 by 20 would be
the sum of these two mixed fractions so
this was the first method where we just
like the next fraction is improper
fraction and then we do the addition
like how we do for like and unlike
fractions now what is this now what is
the second method of adding mixed
fractions so it is have a look at this
method so in this case we add the whole
part separately and the fractional part
separately it's very interesting so
let's take an example let's say you have
to add to 3 by 4 plus 1 1 by 4 so which
is the whole number part so this is the
whole number part for this mixed
fraction this is the whole number part
for this mixed fraction so we add the
whole numbers separately that is 2 plus
1 is added separately and the fractional
part that is 3 by 4 and 1 by 4 these are
added separately so 2 plus 1 is 3 3 by 4
plus
one by four would be 3 plus 1 by 4 so
this is equal to 3 plus 4 by 4 right so
4 by 4 is 1 so this becomes 3 plus 1 so
this becomes 4 so 4 is the answer so
this is one way of adding the whole part
separately and the fractional part
separately so in this case you do not
promote it in to improper fraction let's
look at another example
let's say you have to add to 3 by 4 plus
1 1 by 5 so how do you then again pick
the whole numbers which are 2 and bunch
you are going to be added separately and
3 by 4 and 1 by 5 to be added separately
so 2 plus 1 is 3 and how do you add
these two they are unlike fractures till
you take the LCM so LCM of 4 & 5 is
folding so the denominator in the result
will be 20 now if you convert this into
like fraction you have to multiply 4 to
5 so when you multiply 4 into 5 your
children have to multiply by 5 so this K
is 5 into 4 would give you 20 so in the
numerator also given x 4 so this would
be 4 so this becomes 3 plus 19 by 20 so
now when you add the beach to so how do
you add h2 again the same thing because
both of these are unlike so yet 3 is
like 3 by 1 plus 19 by 20 so you would
follow the same with me red
you take the LCM of margin 20 which is
20 right so 1 into 20 would be 20 and so
so you multiply 1 by 20 so this watch me
we have to multiply by 20 children 60
plus in this case it would be 19 those
21 19 or 21
basically I am converting individual
equivalent fractions and so instead of
doing it separately and just doing it
directly here if you want you can do it
separately first the 60 plus 19 would be
70 19/20 so this would be the answer
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