L11 : Multiply 3 Integers - Integers , Maths, Class 7 Video Lecture - Class 7 | Best Video for Class 7

hello friends this video on integers
part 11 is brought to you by exam for
calm no more fear from exam let us now
see how to be multiplied three integers
still now we have learned about handling
two integers at a time may be a positive
integer with a positive integer or a
positive integer with a negative integer
or a negative with a negative integer
let's see how to be angle three integers
at a time so here also we will take
different scenarios let us first
consider the scenario where we have a
negative integer a positive integer and
a positive integer so let us take an
example let's say - 3 x 2 x 2 so you
have one negative and two positives so
how do we multiply this now this is
pretty simple
because multiplying positive integer
with positive integer will anyways give
you positive result so you can multiply
them first and then you can write it as
4 2 into 2 is 4 now you are left with
two integers again that is a negative
integer and a positive integer what
happens when you multiply a negative at
a positive integer you simply find the
product and put a negative sign so this
is how you could handle this scenario
this was a simpler scenario let's look
at the second scenario where you have
all the three negative integers so
something like this minus 3 x minus 3 x
minus 3 so here you see all of them a
negative integer now it is not necessary
that all the integers need to be the
same integer I am saying that any number
of integers but let's say that there are
3 negative integers so what would happen
so in this case also we will do the same
thing first you multiply the first two
so minus 3 into minus 2 so multiplying
two negative integers you find the
product and put a plus sign so this
would be plus 9 x minus 3 so again you
have the same scenario two integers one
positive one take
so what you do you find the product and
put a minus sign so how much did you get
- 27 now let us say that in case we have
four integers all of them are negative
something like this - three - C and one
more - three so anyways when you talk
about the product product is all about
just so what happens in this case so let
us follow the same process here so minus
3 into minus 3 would be 9 again minus 3
and 2 minus 3 would be 9 so this would
be 81 now do you observe something
whenever three negative numbers you got
a minus sign in the result when there
are four negative numbers you get a plus
sign in the result so and I hope that
you understand why is that happening
because whenever they add two minus
signs the result is a plus sign right so
from this what we conclude is if the
number of negative integers if in case
you are multiplying only negative
integers maybe five negative integers
ten negative integers 6 7 12 15 whatever
number but if the number of negative
integers number of negative integers if
this number is even then the result
would be positive and if the number of
negative integers is odd then that
result could be negative so something of
this sort like here the number of
negative integers was odd one two three
therefore the result was negative here
the number of negative integer is even
one two three four therefore the result
is positive now it is not necessary for
this rule to apply doesn't matter
whether the numbers are the same or they
are different for example if you have
something like - 12 x - 5 x - 2 31 x
minus 30 so if you are multiplying this
so how many numbers - how many digits do
you have
two three four so four that is the
number of negative integer is even
therefore the result would be positive
now what the result would be four that
you will definitely need to find the
product but the sign for the result will
always be positive so this is a very
interesting observation and this is a
very simple tip that you can remember
whenever you are finding products of
integers because as far as finding
products of innocence is concerned the
main problem comes with the sign that
what would be the sign of the result now
let us look at the third scenario where
we see that we have a negative integer a
positive and a negative integer so let
us take this example minus 3 x 2 x minus
6 so you have a negative positive
negative so in this case how do we
proceed we first multiply the two
negative integers let's multiply these
so minus 3 into minus 6 6 3 is 18 and 2
negative sign so it will be positive so
2 into 18 and this is going to be 36
right now in this case also if you try
to apply the last tip that we learned
how many negative integers do we have we
have two negative integers 3 & 6 now the
number of negative integers is even
therefore the result would be positive
so therefore the tip that we need to
follow is variable the number of
negative integers even the product is
positive and when the number of negative
integers is odd the product is always
negative
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