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

hello friends this video on fractions
and decimals part 10 is brought to you
by exam fear calm no more fear from exam
so now let us look at some of the
questions question number one what does
this drawing represent so here you see a
lot of images so the first image so what
what is it you have a square which is
divided into four equal halves out of
which one half is shaded so this
represents one by four but you have
three such squares that means all
together what does it represent 1 by 4
multiplied by 3 so this is what is being
represent by this drawing similarly
let's look at this first let us focus on
the first circle so you have 1 2 3 4 5 5
equal parts out of which 1 part is
shaded that is 1 by 5 but you have 2
such circles so this multiplied by 2 so
1 by 5 into 2 is what is represented by
this drawing let's look at the third one
so here again you have a circle then 2
parts out of 3 parts are shaded so it is
2 by 3 and you have 3 slit circles so
this is 2 by 3 multiplied by 3 question
number 2 what does this drawing
represent so here it actually is telling
you something which results in something
else
okay so let us first focus on the first
triangle what does it show it has four
equal parts 1 2 3 4 out of which 1 2 & 3
parts are shaded so this is 3 by 4 and
how many such diagrams do you have you
have 3 similar triangles that means 3 by
4 multiplied by 3 right now what would
be the result of this 3 by 4 multiplied
by 3 so the result would be the result
actually should be 9 by 4 but let us try
to understand it
from this image so it shows this is
totally shaded so this is completely
shaded so this is going to be four by
four what about this this is also
completely shaded so this is also four
by four but here it is only one part is
shaded so this is one by four so
basically this is 4 by 4 plus 4 by 4
plus 1 by 4 so that means 4 by 4 is 1 4
by 4 again is 1 and 1 by 4 so 1 plus 1
is actually 2 so 2 plus 1 by 4 so how do
we add this so here for now here you
have 1 so 1 into 4 is 4 therefore 2 into
4 plus 4 into 1 is 4 so 1 into 1
therefore 4 2 8 plus 1 1 so 1 divided by
4 so this is 9 by 4 so this represents 9
by 4 so this actually tells that 3 times
3 by 4 is equal to 9 point 4 that is
being represented by this drawing and
this 9 by 4 if you write it in as mixed
fraction it is 2 1 by 4 that means two
triangles are completely shaded and the
third triangle is shaded only 1/4 so we
still have another image so I'm sorry I
have written over it but still I think
it is manageable so here in the first
figure you see there is one part which
is shaded one part out of 1 2 3 4 5
parts so this represents 1 by 5 here
also 1 part out of 5 part here also 1
part out of 5 parts so basically 1 by 5
multiplied by 3 is equal to in this case
you see 1 part 2 part and 3 part so here
3 parts out of 5 parts are shaded so
this represents 3 multiplied by 1 by 5
is equal to 3 by 5 question number 3
multiply and reduce to lowest form see
here we will have a good practice let us
start with the first one it is 20
multiplied
by five by four so how do we multiply
this again numerator with numerator so 5
into 20 is 100 divided by denominator
into the nominator which is 1 into 4
that is 4 so this would be hundred by 4
now you can write it in terms of this
way as 100 by 4 so you can also write it
as if you actually divide hundred by 4
what do you get for twos an 8 2 then you
have 0 5 or 20 so basically four into 25
is equal to hundred right so this one
hundred by four can also be written as
one hundred can be written as 25 into 4
divided by 4 so 4 & 4 will cancel out so
you are left with 25 so 20 multiplied by
5 by 4 is equal to 25 let's look at the
second one that is 2 by 3 into 4 so here
again you multiply the numerators
together so this would be 8 divided by 3
into 1 which is 3 so is it in the lowest
form yes it is already in the lowest
form because if you compare the common
factors of 8 & 3 so what are the factors
of 8 1 2 4 8 and what are the factors of
3 1 & 3 so do you have any common factor
between the two except one no therefore
this is already in the lowest form let's
look at the third one it is 5 into 6 3
by 4 so first of all we will convert the
mixed fraction into improper fraction so
6 into 4 24 plus 3 that is 25 26 27 so
this would be 27 by 4 now multiply the
numerators that is 5 into 27 which is
135 divided by multiply the denominators
that is 1 into 4 which is 4 so 135 by 4
so this is also in its lowest form
because they do not have any common
factor
other than one so this would be the
answer question number four that is 2 by
7 into 7 by 9 so in this case we will do
the same 2 into 7 is 14 and 9 into 7 is
63 so here let us find the common
factors 14 common factor would be 1 2 7
14 and what about 63 for 63 the common
factors would be 1 3 7 9 21 and 63 so
which is the highest common factors the
highest common factor here is 7 so
therefore what we will do we will divide
both the numerator and the denominator
by 7 so 14 divided by 7 is 2 and 63
divided by 7 is 9 so 2 by 9 is the
lowest form let us now look at the fifth
one now we do not have enough space
let's do it here so fifth one is 2 by 3
multiplied by 2 into 2 by 3 so first we
will convert it into improper fractions
that is 3 into 2 6 plus 2 that is 8 so 8
by 3 now again multiplying the
numerators 16 multiplying the
denominators that is 9 now 16 and 9 do
you think we can reduce it to lowest
form we can't because they again do not
have any common factor other than 1 so
this is already in its lowest form so
the answer would be 16 by 9 thank you
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