L2 : Integers - Integers, Mathematics, CBSE Class 6 Video Lecture

[Music]
hello friends this video on integers
part 2 is brought to you by exam feel
calm no more for your prom exam so they
then came up these integers so integers
are a set of numbers which include the
positive numbers plus negative numbers
plus zero so basically it includes all
the whole numbers along with the
negative numbers so all of them together
are called integers so to sum it up we
mean that now when we talk about
integers we talk about all the natural
numbers like 1 to infinity we also
talked about zero that ways we include
all the whole numbers and at the same
time we also include all the negative
numbers so when we represent all of
these on a line which makes the number
line so this is how it looks you have
zero at the center on the right side you
have all the series of positive numbers
on the left side of zero you have all
the negative numbers so this is how the
entire arrangement of integers look like
so this means that integers include them
all the natural numbers they are
included with an integer so you see
these are the natural numbers when you
add the 0 with the natural numbers what
do you get all that is enclosed within
the green sheet that is whole numbers
now when you include the whole numbers
plus the negative numbers then you get
all that is included within the red
shield that is the integers so integers
include the whole numbers natural
numbers negative numbers all of them
together make the integers so natural
numbers whole numbers negative numbers
they are all part of integers now where
how do we locate integers on a number
line so as I said that as long as we
knew only about natural numbers of whole
numbers this is how our number line
looked like so it started with zero and
then it moved on to infinity now that we
also know the negative numbers it
becomes something like this where we
have the negative numbers on the left
hand side of 0 so this this is how the
individuals look on a number line so how
do we locate different integers on the
number line so if you are looking for a
positive integer
then you should definitely move towards
the right of zero for example if you are
looking for +3 then you need to move
right of zero and take 3 jumps like 1 2
3 and that's correct that's how you
reach 3 now let's say that if you want
to reach a negative integer then you
definitely need to move towards the left
like minus 3 would be on the left of 0
so depending on whether you need a
positive or negative integer you need to
make your jumps in the respective
directions now the question comes is how
do we compare integers now earlier we
only had positive number so things were
pretty simple
we knew that ok if a number is with 3
digit a three-digit number will always
be greater than a two digit number and
so in new things and it was pretty much
simple now that we have both negative
and positive numbers so the comparison
might become a little difficult though I
will not make it difficult for you but
it might sound a little difficult that
is comparing minus 16 with plus 6 which
would be greater or comparing minus 16
with - hundred which would be greater so
you know when you have this negative
sign into place will things become more
complex let's find that out so let us
look at some examples first so you have
10 and 18 if I ask you which is bigger
10 or 18 now very quickly I am sure you
would answer that 18 is bigger than 10
so this would be a pretty simple
question for you to answer which is
bigger 10 or 18 so obviously you would
say teen is bigger than 10 now when you
look at the number line so let us make a
rough number I may have 0 1 2 3 4 5 and
so on now we are only focusing on the
positive numbers because both 10 and 18
are positive so let's say you have 10
somewhere here and then you have
anything somewhere here so we are not
plotting all the numbers 10 18 so when
you look at this you see 10 comes here
and 18 lies all the mode on the right of
10 so very clearly looking at the number
line also
can say that okay 18 is greater than 10
now things turn a little different when
you have one positive number and the
other negative number for example if you
have to decide amongst minus 35 and plus
31 which is bigger so how would you
decide in that case because one is
negative and the other one is positive
now again there is focus on the number
line now one important thing is that all
the positive numbers now gradually have
you seen one thing that as you move
towards the right on the number line
what happens the values increase like 7
is greater than 2 18 is greater than 7
right so as you keep moving towards
right the values keep increasing now
this is true not only for the positive
integer this is true for the entire
number line so on the number line the
moment you move towards right your
values keep increasing now when you look
at the negative number sign what happens
here in this case as you move towards
right you are actually moving towards
numbers length minus 1 is 2 minus 3 and
so on and these numbers are greater than
numbers 8 minus 99 or minus 100 because
they are located towards this side so
now when you look at the negative number
aisle you you can see that you have
numbers pleased like this so minus 10
and minus 2 if you try to compare these
two which is bigger so my image 2 is
bigger because minus 2 is located on the
right of minus 10 and as you move
towards right the value increases right
so basically if you now focus only on
the negative numbers you see that in
case of negative numbers if you compare
minus 10 and minus - even though tenures
bigger than 2 but minus 10 is smaller
than minus 2 so the moment you put minus
sign there values
but I mean the relationship between the
two integers completely traverses so in
this case one number is negative the
other number is positive not quite
obvious all the positive numbers are
located on the right side of the
negative numbers therefore all positive
numbers are greater than negative
numbers so in this case also 31 will be
greater than minus 35 let's look at this
example here you have 103 or minus 108
so again in this case the positive
number would be greater than the
negative number as I discussed now let
us try to understand the comparison
between two negative numbers minus 35
and minus 31 which one is greater so as
such if you forget about a negative sign
then 35 is later than 31 but the moment
I put negative sign to both the numbers
the relationship becomes opposite so we
say that mine will scatter 5 is smaller
than minus 31 but why so I have already
proved that using number line that on a
number line anything that is on the
right is greater so minus 31 is of the
right of minus 35 so it up later now let
us think and a real-life example and try
to understand why we minus 25 is smaller
than minus can be 1 now let's take the
example of temperature so let's say that
you have gone to a hill station which is
very cold and moreover it is winter
season peak winters so in each passing
day the temperature is dropping further
so initially the temperature was around
10 degree Celsius after a couple of days
it dropped to zero degree thing 2 minus
5 degree minus 10 degree and finally it
dropped to as low as minus 31 degree
Celsius now what is happening now as the
temperature is dropping further so the
decrease is more at night so what is
happening so as it decreased to minus 31
when it further decreased it became
minus 35 that means minus 35 is smaller
than minus 31 logically also it is
smaller right so please do not keep this
confusion in your head that 35 is
greater than 31 that's fine
both of them are positive numbers so we
are only bothered about air values but
the moment you put a negative sign to
them the relationship becomes just the
opposite so minus 31 becomes greater
than minus 35 so when you place it on a
number line very simple thing that you
need to remember is as you move towards
right you move towards bigger number
that is the only thing you need to
remember so whenever you are comparing a
positive number and a negative number
the positive number would be greater if
you are comparing two negative numbers
or two positive numbers just follow this
rule going towards right would mean a
bigger nun
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