Examples: Multiplication of a Fraction by a Fraction Video Lecture | Advance Learner Course: Mathematics (Maths) Class 6

hello friends this video on fractions
and decimals part 11 is brought to you
by exam fear calm no more fear from exam
question number 4 which is greater to
buy seven of three by four or three by
five of five by eight
now first of all let us understand what
do we mean by two by seven of three by
four this basically means 2 by 7
multiplied by 3 by 4 so let's multiply
the numerators it is 3 to 6 let's
multiply the denominators it is 7 for 28
so this is 6 by 28 so we can reduce it
to its lowest form so how can we reduce
it so let's write the factors of 6 1 2 3
& 6
let's write the factors of 28 that is 1
2 7 14 4 and 28 so these are the factors
so which is the highest common factor so
the highest common factor here is 2 so
their food we divide the numerator and
the denominator by 2
so 6 divided by 2 would be 3 and 28
divided by 2 would be 14 so 2 by 7 or 3
by 4 is going to be 3 by 14 so this is
one fraction which needs to be compared
the other fact fraction that needs to be
compared is 3 by 5 of 5 by 8 which is
equal to 3 by 5 in to 5 by 8 so this is
equal to 15 by 40 so again if you look
at their factors 15 is 1 3 5 and 15 and
40 is 1 to 5 for 10 8 20 and 40 so which
is the highest common factor it is 5 so
their food we will divide the
and the denominator by five so this
would be three and 40 divided by 5 would
be 8 so this value would be 3 by 8 so
now basically we have to determine
whether 3 by 4 in is greater or 3 by 8
is greater now when you compare these
two you see that these are unlike
fractions that is they have different
denominators
so what we need to do we need to ensure
that we convert them into such fractions
such that they both have same
denominators so in order to do that we
will take the LCM of both the
denominators right so we take LCM of 8
and 14 and what is the LCM of 8 and 14
let's find out so let's say 8 + 14 - 4 8
- 7 - 14 - 2 so 4 this is 7 to 1 - this
is 7 and then 7 1 1 so basically the LCM
would be 7 into 2 into 2 into 2 which is
equal to 56 7 to the 14 14 to 28 28 into
256 so LCM of 8 and 14 is 56 so now let
us try to convert these two fractions
into fractions which have same
denominator 1 is 3 by 40 the other is 3
by 8 so this 3 by 14 we multiply the
numerator and denominator with the same
whole number such that the result has a
denominator 56 and the same thing we do
it for 3 by 8 as well so 14 into 4 is 56
therefore we multiply the numerator also
by 4 so we get 12 by 56 8 into 7 is 56
so we multiply the numerator also with 7
solving it 21 by 56 now it is very easy
to compare these two one value is 12 by
56 and the other one is 21 by 56 now we
know that 21 is greater than 12
therefore
they won by fifty six is greater than
twelve by fifty six so twenty-one by
fifty six is nothing but three by eight
so three by eight is greater than three
by fourteen question number five
Sally plants four saplings in a row in
her garden the distance between two
adjacent saplings is 3 by 4 meters find
the distance between the first and the
last sapling so the question tries to
say something like this let's say this
is one sapling this is another sapling
this is yet another sapling and this is
the fourth sapling so Sally has planted
these four saplings in one row one after
another such that the distance between
two adjacent saplings let's say the
first sapling and the second sapling
distance is 3 by 4 you can say in then
third sapling distance is 3 by 4 third
and fourth again the distance is 3 by 4
now the question is find the distance
between the first and the last sapling
so this is the first sapling this is
where the last sapling is so we have to
find out this entire distance so how
would you find out this entire distance
this entire distance is nothing but 3 by
4 plus 3 by 4 plus 3 by 4 which actually
means that tree by food is added three
times which can be written as 3 by 4
into 3 so if you multiply the numerators
which is 9 we multiply the denominators
which is 4 so the distance between the
first and the last sapling is 9 by 4
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