L1 : Introduction - Comparing Quantities , Maths, Class 7 Video Lecture

hello friends this video on comparing
quantities part 1 is brought to you by
exam feel calm no more fear from exam
topics to be covered in this lesson our
introduction comparing quantities ratio
percentage conversion of percentage into
fractions conversion of fractions ratios
and decimals into percentages increase
or decrease as percent price is related
to buying and selling of items profit or
loss percentage principal amount and
simple interest sometimes it happens
that you stand with your elder or
younger sibling and you ask who is
taller out of the two of you so what are
you trying to ask basically whose height
is more so basically you are trying to
compare your height with that of your
sister so let us say that if your sister
is saying 138 centimeters tall let's say
that that's the height of your sister
and your height is 125 centimeters so
this is you and this is your elder
sister so these are your heights now
when you ask who is taller what are you
trying to ask basically whose height is
more so you are basically trying to
compare these two numbers 138 and 125 so
out of these two numbers whichever is
more that person is taller similarly
sometimes once you get your report card
you tend to compare it with somebody in
your neighborhood maybe a friend who is
studied in a different school so he had
appeared in a different examination
conducted by a different school so you
see that when you look at your report
card
you have scored 70 out of 100 when you
look at your friends report card you see
that he has scored 80 which is
definitely more than 70 but he has coded
out of 200 now if you want to compare
that who scored better on who performed
the bass better because in this case you
just can't compare 70 and 80 even though
self 80 is greater than 70 but we just
can't compare the numerators right in
this case both of these are fractions so
you have a numerator you have a
denominator now since the denominator in
both the cases are different because the
total marks out of which the examination
was conducted was different for your
school and your friends school so how
would you compare this now in the report
card in one corner you have seen that
your total score is expressed as
percentage where it sees that you have
scored 70% marks similarly for you in
your friends report card it says that
your friend has scored 40% marks now
when you look at this that is when you
realize that you have actually performed
better even though if the total marks
scored by you is lesser than your friend
but overall you scored a better
percentage than your friend so that way
you can see that you performed better
than your friend now in each of these
examples what were we actually trying to
do we were trying to compare quantities
so in the first example we were trying
to compare height of your sister and
yours in the second example we were
trying to compare the score of yours
with that of your friend so in this
lesson we will learn more about
comparing quantities that is what are
what are the various ways by which we
can compare two different quantities let
us look at another example so here on
the screen you see three fits now let us
name them let us call them a B and C so
these are the three kids and all of them
are hungry each of them is given a pizza
as you can see on the screen so each of
them have been given a pizza of the same
size now the entire pizza
if you cut that pizza to equal slices
then you get five equal slices like that
is also visible on the screen one two
three four and five so if you divide it
equally into five equal slices this is
how it would be and each of this pizza
is given to all the three kids now it is
observed that he eats one slice out of
the five slices so basically a eats
one-fifth of the pizza when it comes to
B it is seen that B eats three out of
the five slices so he eats three fifth
of the pizza when it comes to see he
eats four slices out of the five slices
so he eats four fifth of the pizza now
if you are asked that can you tell me
who ate more now that's quite evident
because C ate four slices of the pizza
so food is greater than three which in
turn is greater than one right so we
observe that 4 is greater than 3 which
is greater than one therefore 4 by 5 is
greater than 3 by 5 which in turn is
greater than 1 by 5 now why can't we
just compare the numerators in this case
because the denominators were same so
all of them have the same denominators
so that means we can see that 4 by 5 is
greater than 3 by 5 is greater than 1 by
5 so that means we can say that C ate
maximum and a ate minimum so what what
did I do here in this example here again
we tried to come their fractions so 1 by
5 3 by 5 4 by 5 these are all fractions
and we just try to compare the fractions
to find out which one is bigger and
which one is smaller so this is yet
another example where we are trying to
compare quantities let's look at another
interesting example so what do you see
on the screen you see a couple going on
a trip a road trip in their car now they
start from their home thinking that
they'll go on a long drive now it's
quite difficult for one person to drive
then
I earn distance because that that's a
long distance so what the decide is the
wife let's call them mr. and mrs. Smith
so let's give them a fancy name now mrs.
Smith she drove for 3/4 of the distance
so whatever the total distance was she
covered 3/4 of that entire distance and
mr. Smith covered the remaining 1/4 of
the distance so that's how they divided
their driving amongst each other so that
unit none of them should get stressed
out now if you are asked that who
covered maximum distance who drove for
the major part of the distance whether
it was mr. Smith or it was mrs. Smith so
basically we again need to compare two
fractions one is 3 by 4 and the other
one is 1 by 4 right so again we know 3
by 4 is greater than 1 by 4 because the
new denominators are the same and the
numerator 3 is greater than the
numerator 1 therefore we can say that
mrs. Smith drove or mrs. Smith covered
more distance so again so here what are
we comparing we are comparing the
distance now instead of saying 3/4 of
the distance or 1/4 of the resistance we
could have also mentioned it like this
that maybe mrs. Smith she covered 775
kilometers and mr. Smith covered 25
kilometers and the total distance they
actually traveled 100 kilometers so mrs.
Smith covered 75 kilometers and mr.
Smith covered 25 kilometers so that
would again mean the same thing so
basically what are we trying to compare
here
so we are comparing distance in this
case we were comparing fractions so
doesn't matter whether these are
integers or fractions but when we try to
compare two quantities we should be able
to compare any number with another you
think from a shopkeepers point of view
let's say that you are observing two
different shopkeeper shopkeepers one
shopkeeper one and
- so let's say that shopkeeper 1 & 2
they are selling different items maybe
shopkeeper 1 is selling stationary items
maybe shopkeeper 2 will sell in grocery
item so they are actually selling
different items at different rates and
both of them are making some profit so
let's say the shopkeeper 1 is making a
profit of 12% and shopkeeper 2 is making
a profit of 11% now what do we mean by
12 percent profit 11 percent profit that
basically means that a any shopkeeper
whenever he sells some Goods he also
buys those goods from some other
wholesale market like that that's how
the real scenario works so basically he
also pays a price and buyers who buys
those things and then he sells them at a
higher price and that's how he makes
profit so the here 12th person and 11
person they indicate the percentage of
profit that they make so instead of
writing like the first shopkeeper makes
twelve thousand Crawford so instead of
saying that if you see it he makes
twelve percent profit so that is like
more sensible and more generic to
express how much profit the shopkeeper
is making however in this chapter itself
we are going to talk about profit
percentage in more detail so there you
will understand what exactly is profit
percentage now here in this example if
this is the data given to you the
shopkeeper one makes twelve percent
profit shopping to make eleven percent
profit now if you are asked that who is
making more profit one or two so what
will you compare so you will basically
compare these two percentages that is 12
percent 11 percent and you find that -
twelve percent is greater than 11
percent therefore you would say the
shopkeeper one is making more profits so
in this case what will be compared so we
compared percentages here so that's what
I was telling you that if there are
various ways by which you can compare
two different quantities thank you
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