Examples: Proportion Video Lecture - Class 6

hello friends this video on ratio and
proportion part 12 is brought to you by
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get a few questions now question number
one right true or false
21 is 2 6 is proportional to 35 is 210
so for this we need to find out the
values of each of the ratio so first
let's calculate 21 is 2 6 which is equal
to 21 by 6
now hcf of 21 + 6 is 3 so divide the
numerator and denominator by 3 so this
becomes 7 by 2 so in a similar fashion
we do it for 35 is 210 which is equal to
35 by 10 so the HCF of 35 + 10 is 5 so
divide the numerator and denominator by
5 so it becomes 7 by 2 so both are equal
therefore this is true now I am NOT
finding out the HCF for all the numbers
because I have already taught you how to
find the HCL so you can do that part on
your own let's look at the next one 0.9
is to 0.36 is proportional to 10 is to 4
so let's calculate this ratio first 0.9
is to 0.36 so this would be equal to 0.9
by 0.36 so we all know that a 0.9 can be
written as 9/10 that's because after the
decimal point you have one digit so
therefore after one you will have one
zero similarly 0.36 can be written as
three six divided by 100 because after
the decimal point you have two digits so
that 100 will come here so this is how
you can write this so this becomes 10
into 10 is hundred 9 into 4 is 36
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and in Toulouse a four and five in
sustain so this is equal to 5 by 2 so
basically what we have done in the
Stan's relation is nothing but just the
same thing like how we find the Hz if
you want you can find the HDF of 90 and
36 and then you know you can say it
would be 18 and then also you will get 5
by 2 in a similar way let's calculate
this ratio that is 10 is 2 4 which can
be written as 10 divided by 4
now the HCF of 10 and 4 is 2 so let's
divide the numerator and denominator by
2 which makes it 5 by 2 so in this case
also the values of the two ratios are
the same therefore this is also true
question number 2 are the following
statements true 7.5 liters is 215 liters
is equal to 5 kgs is equal to say 5 kgs
is 2 10 kgs so let us try to find out
the value of each of these ratios first
this one and then this one so let us
first work on 7.5 liters is 215 liters
so this can be written as 7.5 divided by
15
now 7.5 can be written as 75 by 10 so
this would be 150 because 15 into 10
would be 150 now this by prime factorize
a should 75 can be written as 5 into 5
into 3 150 can be written as 5 into 5
into 3 into 2 so the 5 5 will cancel 3 3
would cancel so you are left with 1 by 2
so that's the value which you get from
left hand side now let's focus on the
right hand side that is 5 kgs is 2 10
kgs so this is equal to 5 by 10 now if
you divide it by 5 numerator and
because fire is a itself so you get 1 by
2 so here also you get 1 by 2 so
therefore this statement is true let's
look at the next one 32 meters is 264
meters so let's calculate how much is
this 32 meters is 264 meters can be
written as 32 by 64 now again 32 can be
written as 2 into 2 into 2 into 2 into 2
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64 can be written as 2 into 2 into 2
into 2 into 2 into 2 so here this 2 & 2
will cancel so all these twos will
cancel so this would be 1 by 2 so 32 by
60 2 will be 1 by 2 now let us try to do
the calculation for right hand side that
the 6 seconds to 12 seconds so 6 seconds
is 2 12 seconds can be written as 6 by
12 so now here if you divide the
numerator and denominator by 8 CF it is
1 by 2 so both are equal so that means
the left hand side is equal to the right
hand side so this is also true we will
now focus a little bit on problem
solving how do we solve problems from
our day-to-day life let's look at the
simple scenario let's say that if a book
costs rupees 50 so cost of one book is
rupees 50 and you have to find out the
cost of 8 such books so how do you think
you will find it out and that's very
easy right what you will do is 8 books
each book is 50 so you just multiply 8
and 50 and you get it as 400 so you
calculate that 400 would be the cost of
8 books so this is a simple scenario now
instead of this if it was given to you
the cost of three books is rupees fifty
so the cost of one book is not fifty
instead three books cost is rupees fifty
and you have to find out the cost of
eight books so in this case how are you
going to find it out so that is when you
are given the cost for multiple books
and you also need to find out the cost
for multiple books maybe some other
number like here three books cost is
given eight books cost you have to find
out so in these kind of situations we
make use of uni tree method so what is
this uni
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