Representation of Fractions' Multiplication using Shapes Video Lecture - Class 7

hello friends this video on fractions
and decimals part eight is brought to
you by exam for calm know about fear
from exam now let us look at a
representation of different fractions so
what are we going to do now is we look
at pictures and looking at the pictures
we will tell what fraction is it trying
to represent now here what do you see
you see a circle divided into how many
equal parts divided into one two three
four five six seven eight
eight equal halves and you see some part
of the circle is shaded so what we are
we want to do here is how much is the
shaded part of the total part what
fraction of this diagram is shaded so
the shaded part is shaded in black or
green whatever you call it so how much
part is shaded out of the eight equal
halves how many halves are shaded one
half right so only this half is shaded
so one part out of eight parts this
shaded so we can see that one eighth of
the circle is shaded so one eighth of
the circle is shaded let us look at this
triangle so this triangle has been
divided into how many equal halves
one two three so total there are three
halves and how many parts out of three
are shaded one so one-third of this
triangle is shaded let's look at not yet
another figure so here this is a
rectangle so here it has been divided
into four equal parts and one part out
of the four parts is shaded so one
fourth of the rectangle is shaded so you
know this is how looking at pictures you
should be able to identify what fraction
of that picture is shaded or not shaded
now
look at similar figures in a little
different way so in this case you can
see that the the portion which was
shaded has changed right so in the first
case you have a triangle and what how
many halves are shaded now so here also
you see that the triangle is divided
into three equal parts and out of this
three equal parts two parts are shaded
so 2/3 of the triangle is shaded
look at this rectangles it has eight
equal parts
how many shaded one two three so three
out of four because it has four equal
parts and out of four three are shaded
so we say that 3/4 of the rectangle is
shaded look at this circle now here how
many has shaded one two three four five
five are shaded out of how many out of
one two three four five six seven eight
so five eight of the circle is shaded
so you see why am i taking so many
examples is to make you understand how
do we determine what part is how what
part of the entire thing is shaded or
what part is not shaded for that matter
now if I ask you this is the portion of
the circle which is shaded 5/8 of it if
I ask you what fraction of this circle
is not shaded how would you answer that
so how many parts are not shaded one two
three so these are the three parts which
are not shaded so three out of eight so
three eight of the circle is not shaded
now here we are going to do something
more interesting so we learned how to
multiply fractions right so here we are
representing fractions multiplication
using these figures so what do you see
so let's look at the first set of figure
so what do we see we see three triangles
exactly identical to each other and each
triangle is
divided into three equal halves and what
part of this triangle is shaded so 2/3
of the triangle is shaded here here also
2/3 of the triangle is shaded and here
also 2/3 of the triangle is shaded now
you have three similar triangles there
to third part is shaded so basically
this means that we are trying to add
these 2/3 of a triangle plus 2/3 of a
triangle plus 2/3 of a triangle so what
are we actually doing we are adding 2 by
3 2 by 3 is added 3 times so that
basically means 2 by 3 multiplied by 3
so 3 means 3 by 1 so what would be the
result
so numerator multiplied by numerator so
6 divided by denominator multiplied by
denominator that is 3 and we know that 3
into 2 is 6 so this is equal to 2 so
whether it is 6 by 3 or 2 so the result
is shown in this fashion so here what do
you see in this image you see that all
the 3 parts are shaded so basically this
is 3 by 3 what do you see here here also
all the 3 parts are shaded so this is 3
by 3 and here 0 part is shaded so it is
0 by 3 so again when you add these 3
what do you get so it is 3 by 3 plus 3
by 3 plus 0 so this is equal to 6 by 3
so this is the same thing which you got
here 6 by 3 6 by 3 so basically this
this was 3 what does this represent
together this represents 3 into 2 by 3
and what did this represent this
represents the result correct so
basically when you look at this or when
you look at this they actually represent
the product this represents the result
of the product and this represents the
fractions which are getting multiplied
so this is a representation of factors
multiplication
so let us look at to get another example
so here what do you see you see two
circles in the first circle five parts
out of eight parts are shaded one two
three four five and the same is true for
the next circle as well so when you add
these two what are you going to get so
adding be used to basically means that
five by eight multiplied by two so what
would be the result the result would be
10 by eight so how can we represent the
result that means ten parts out of eight
parts what does that mean now you might
ask that when there are totally eight
parts then how can we have ten shaded
parts this basically means that out of
these two because you started with two
circles so you still have two circles so
in these two circles total you have ten
shaded parts so the first circle is
totally shaded and in the second circle
you just have two parts shaded do you
want to see another interesting thing
can you this is right now an improper
fraction if you convert it into mixed
fraction what do you get you divide 10
by 8 so 8 ones are 8 and the remainder
is 2 so 10 by 8 can also be written as 1
2 by 8 and don't you think that that is
what is exactly represented by these two
one that means one complete circle is
shaded so this circle is completely
shaded so that is represented by one and
two by eight that means the other circle
in the other circle only two part out of
eight parts this shaded so one two by
eight is exactly what is being
represented by these images so this is
how we can represent factors
multiplication using images thank you
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