Rules for Arithmetic: Use of Variables Video Lecture - Class 6

hello friends this video on algebra part
7 is brought to you by exam feel calm no
more fear from exam how do we use
arithmetic rules with variables like
when you deal with numbers you see that
numbers are commutative in addition that
is 1 plus 3 is equal to 3 plus 1
similarly we talked about many of the
properties like associative property
distributive property now do these
properties hold true for variables as
well so let us have a quick look so when
you talk about commutative property it
sees this commutative property exists
for both addition as well as
multiplication so how does it work for
numbers well for numbers it is something
like this let's say you have two numbers
2 & 5 so 2 plus 5 will be equal to 5
plus 2 and if you actually try to find
their sum you would see that in both the
cases the sum is 7 so it doesn't matter
what is the order of the two numbers
whether 2 is before or 5 is before that
doesn't matter but this their sum would
always remain the same similarly
community compatibility for
multiplication would be 2 into 5 is
equal to 5 into 2 again this in this
case also the order doesn't matter
product of two numbers would always
remain the same now what in case of
variables so for variables also if you
have two variables a and B a plus B is
equal to B plus a similarly if you have
two variables a and B a into B is also
equal to B into a so that means this
rule holds true for variables also that
is the order of the variables does not
matter the sum of two variables remains
the same similarly the product of two
variables is the same whether you I
don't change their order similarly if
you talk about associative property
again associative property exists for
addition as well as multiplication so
when it comes to addition for numbers
let's first talk about the numbers
because for numbers you have
I learnt about all these properties so
if you have three numbers let's say 2 3
& 4 so as per the associative property
it says that 2 plus 3 plus 4 is equal to
2 plus 3 plus 4 so whether you first add
the second and third number and then add
the sum to the first number or you add
the first and second number and then add
the sum to the third number so the
result would be the same for example if
you try to solve this side left-hand
side you would see it is 2 plus 7 which
is equal to 9
similarly if you try to solve this one
you would see 2 plus 3 is 5 plus 4 so 5
plus 4 is 9 so the result is the same in
both the cases so again this also proves
in a way that if you have three numbers
it doesn't matter which two numbers you
add first because overall result is
going to be the same similarly in case
of multiplication also it says more unn
is the same thing just that addition is
replaced with multiplication it says
that if you have 3 numbers 2 3 & 4 then
2 into 3 into 4 is equal to 2 into 3
into 4 that means first you find product
of settings and third number and then
multiply it by 2 so this if you solve it
it becomes 2 into 12 which is equal to
24 in this case if you try to solve it
it is 6 into 4 which is equal to 24 so
the result is the same
and these rules hold true for variables
as well so if you have two variables a B
and C so if you have three variables
basically so you would need a B and C
then you can say that a plus B plus C is
equal to a plus B plus C so this holds
true for variables in a similar way for
multiplication a into B into C is equal
to a into B
to see so it's like the same concept or
the same property exists for variables
as it exists for numbers at least in
these properties like the commutative
property and the associative property
similarly we will talk about another
property that is the distributive
property so let's recall the
distributive property for numbers so as
per distributive property if you have
three numbers let's say you have 2 3 & 5
so these are the three numbers that you
have so for these three numbers if you
have something like 2 into 3 plus 5 that
is one number is multiplied to the sum
of the other two numbers then this
becomes equal to 2 into 3 plus 2 into 5
that is why it is called distributive
property because 2 gets distributed to
both the numbers 3 & 5
so that's that's why the name
distributive property and then you solve
this so you would see that in this case
if you actually try to solve both the
sides in these two different ways the
result would be the same for example if
you write it like this 2 x - 3 plus 5 is
8 so this is 16 in this case 3 to the 6
5 to the 10 so this is 16 it is just
that this process makes it a little
simpler so this is the property for
numbers so the same property holds true
for variables also so if you have three
variables a B and C then a into B plus C
is equal to a into B plus a 2 C so like
for variables also this holds true so
you see that increase of variables now
one important thing that I would like to
mention here is when I say that these
properties hold true for variables that
does not mean that you can add B plus C
because basically the addition and
multiplication of variable
and constants are very different for
example here three plus five could be
added but here you cannot add B and C
together so B plus C will always be B
plus C so what I mean to say is this
entire thing which is true for all the
constants can be very well represented
in the form of variables so the formula
is basically represented using variables
or using algebra so when you look at all
these arithmetic rules whether you talk
about the commutative property or the
associative property or the distributive
property the property is always written
in the form of a formula or in the form
of a rule and the rule is always written
using variables to the rule so anywhere
you want to generalize any rule you make
use of variables so that is the role of
variables and that is why we make use of
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