Multiplicative Identity for Rational Numbers Video Lecture - Class 8

let us look at the multiplicative
identity of a rational number right
before I go through this text I will
just explain to you what does this mean
now you know you can have any rational
number let's say 2 upon 3 4 upon 7 6
upon 8 9 upon 7 okay and so on right now
a multiplicative identity ok basically
means what number should I multiply this
let's call this as X okay such that the
result or the output is actually the
number itself so the answer should be 2
by 3 right
what is the number where by which I
should multiply this particular rational
number to get 2 by 3 similarly 4 4 by 7
what should be the number through which
I should multiply this says that the
result comes as 4 by 7 right now you
must be thinking this is so easy right
because if we have to get the same
number the only thing I need to do is I
need to just remove this X I need to
multiply it by 1 same goes here
multiplied by 1 why because we know that
any number any number multiplied by 1 ok
gives the number itself now how does it
make a difference if this number is
actually a rational number right and
that's the simple truth behind this
thing so 1 is the multiplicative
identity for rational number this is
because if we multiply any number any
rational number by 1 then we will get
the same number so let's say in 6 by 8
if I multiply it by 1 I get 6 upon 8
again if I multiply this by 1 I get 6
upon 8 one interesting thing here is
that you know one can always be written
as X upon X where X can take any value
right so even if you multiply 9 by 7
by let's say 10 upon 10 that also gives
you the identity for this because 10 by
10 is equal to 1 right so that's what we
know about the multiplicative identity
of a rational number