Examples: Division of Integers Video Lecture | Advance Learner Course: Mathematics (Maths) Class 6

hello friends this video on integers but
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all the properties of division let us
look at some of the questions quickly
question number one evaluate - 31 / - 30
+ -1 now we know that division for
division distributive property doesn't
hold true so we will not apply any
property and just we will simplify it
directly so this is divided by minus 30
plus minus 1 which would be minus 31 so
minus 31 by - 31 would be 1 so 1 is the
answer
evaluate - 6 plus 5 divided by -2 + 1 so
let us first solve this so - 6 + 5 would
be -1 divided by minus 2 plus 1 again
would be minus 1 so minus 1 divided by
minus 1 is nothing but 1 question number
3 again evaluate - 36 divided by minus 9
so two negative numbers so the result
would be positive and the result would
be 4 because 9 - 4 is 36 so this would
be + 4 second one 0 / - 12 now 0 divided
by anything is equal to 0 so 0 would be
the answer question number 4 fill in the
blanks 369 divided by what gives 369 so
what does that number which divides any
other number and it retains the same
number yes it is 1 - 206 / - is equal to
1 now what does that number again which
when divided by itself gives 1 every
number you divide any number by itself
you get one that is because 1 is the
multiplicative identity
for example if you divide if you ask two
divided by two is what that means what
is that number with which when 2 is
multiplied abuse 2 so the multiplicative
identity for any number it is 1 that
means 2 1 multiplied by 1 is 2 so we
ready 5 when x 1 2 is 5 15 when x 1 is
15 so 1 is that number which when
divided by any number gives the same
number therefore when you divide two
numbers which are the same then the
result is always 1 - divided by 1 is
minus 87 this is definitely - 87 because
any number divided by 1 gives the same
number 20 / - gives -2 so what is that
number which when multiplied by 2 would
give 2010 and this is going to be minus
10 because there is at this negative so
one of these numbers should be negative
question number 5 the temperature at
12noon was 10 degree celsius above zero
if it decreases at the rate of 2 degree
Celsius per hour until midnight at what
time would the temperature be 8 degree
section below zero what would be the
temperature at midnight so what is given
in the question it is told that at 12
noon the temperature was 10 degree
Celsius above zero that means plus 10
degree Celsius right and it decreases at
the rate of 2 degree Celsius per hour
that means every one hour 2 degree
Celsius decreases there that means if at
12 noon it was 10 degree Celsius at at 1
p.m. it would be 10 minus 2 that is a 2
degree Celsius right again at 2:00 p.m.
what would be the temperature it would
be 8 minus 6 8 minus 2 which is nothing
but 6 degree Celsius and so on so in
this fashion the temperature continues
to decrease so now the quest
yes there will be a time when the
temperature will be a degree Celsius
below zero so a degree Celsius below
zero that actually means minus eight
Dearing Celsius do we have to find out
this eight degree Celsius will happen at
what time so that is what we have to
calculate now let us assume but looking
at this what do we see how at what
pattern is the temperature reducing so
you see at one p.m. it was 10 minus 2 at
2 p.m. it was basically 8 minus 2 which
is nothing but this can be written as 10
minus 2 into 2 again at 3 p.m. if you
see the temperature would have been 4
degree Celsius which would have been
basically 6 minus 2 which can be written
as 10 minus 2 into 3 right so you see it
is following a pattern the degrees is
following a specific pattern now what we
want to know we want to know at what
time it will be minus 80 degree Celsius
now very well you can just continue this
table and you can see the time when it
becomes minus 80 degree Celsius but let
us try to do it a little smartly let us
try to make use of simple equations here
so by now you all have learnt about
equations thing so let's see how we make
use of equations so let us say that this
8 degree Celsius this will also happen
in the same pattern
it happens at 10 minus 2 into T that
means basically it happens after T hours
from 12 noon in this case this
temperature 8 degree Celsius it happened
after one hour from 12 noon that is why
you have 1 here this temperature 6
degree Celsius happened after two hours
from 12 noon that is why you have to
here 4 degree Celsius happen after three
hours from 12 noon that
so you have three here so let us assume
that the temperature reaches minus
eighty degree Celsius after T hours from
12 noon right so let us see 10 minus 2 T
is equal to minus 8 that that would be
our equation right because as per our
assumption the temperature at this point
should be 10 minus 2 T and this is
should be actually equal to minus 8 so
if you solve this equation this would be
10 plus 8 is equal to 2t when you ship
2t to this side the sign changes when
you shift 8 to this side the sign
changes again so this is 18 is equal to
2t now when you shift to 2 this side
again the sign the this is
multiplication and here it will get
divided by 2 so 18 by 2 is equal to T so
two nines are 18 therefore you can say
that thing is equal to 9 hours that
means after 9 hours from 12 noon the
temperature would be a degree Celsius
that means what would be the time at
that time it would be 9 p.m. so 9 p.m.
is the correct answer what would be the
temperature at midnight that means what
would be the temperature at 12 o clock
at night so how will you find that now
at 9 o clock it is 10 minus 2 into 9 so
at 12 midnight the temperature would be
10 minus 2 into 12 that is 10 minus 24
which is equal to minus 14 degree
Celsius so this would be the temperature
at midnight now a many of you might feel
that I have followed a complicated
process but why I did this was so that
you get to know the use of equations how
do we use equations to solve problems if
you want to solve it in a simpler way
without involving equations you can very
well do it in this fashion like how I
was doing
1:00 p.m. 2:00 p.m. 3 p.m. 4 p.m. 5 p.m.
6 p.m. 7 p.m.
so on and then you would have also
concluded reached at 9 p.m.
question number six and elevator
descends into a mineshaft at the rate of
6 meters per minute if the descent
starts from 8 meters above the ground
level so let us say this is the ground
level so the decent starts from 10
meters above the ground so somewhere
here let us say this is a point which is
at a distance 10 meters how long will it
take to reach minus 350 meters below the
ground so that means below the ground it
wants to reach somewhere very below
which is safe some 350 meters below the
ground so how much time will it take for
this elevator to reach from this point
to this point so that is what we have to
find now it starts at 10 meters now what
happens after 1 minute because after
every minute the rate is decreasing
right so after 1 minute where is it
after 1 minute it will be somewhere at
10 minus 6 meters right where will it be
after 2 minutes so after 2 minutes it
would be somewhere 10 minus 6 into 2
after 3 minutes where will it be it will
be somewhere 10 minus 6 into 3 and so on
right now why am i multiplying it this
way because when it started it was a 10
meter after 1 minute it would have
covered some 6 meters because it is
covering 6 meters every minute so it
will be at 10 minus 6 meters right so
take from 10 you subtract 6 meters it
will be somewhere here again after 1
minute it will cover some 6 meters so
that will basically be 10 minus 2 times
six meters it has covered after three
minutes it would have covered three
times six meters so 10 minus 6 into 3
like so we have to find out after what
time so let us say that after time P it
reaches this point so that means 10
minus 6 into T will be equal to 350 -
350 so therefore we can say 10 minus six
T is equal to minus 350 or 360 is equal
to 60 or T is equal to 3 16 divided by 6
so this is 60 so we can say that after
16 minutes it will reach the point which
is 315 meter below the ground level
right so this is the approach that you
should follow to solve problems so
anywhere you look at the problem draw a
rough figure try to understand what it
is saying and then try to follow an
approach to solve it so I hope that this
lesson on integers would have helped you
so it is not only about learning the
properties of integers but also trying
to apply them in day to day life in day
to day problems so here you have learned
the multiplication and division parts of
integers which are which when you try to
solve more and more problems and durm
that would actually help you to get your
concepts killed so I hope this lesson
would have helped you see you all in the
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