One as a Multiplicative Identity.
A boy was given maths homework to solve.
The homework consisted few multiplication questions.
The boy being a student of Toppr found the multiplications very easy.
Next day, the teacher asked the boy if he observed any similar pattern in the homework
On being asked such a question, the boy again sits back and concentrates on the questions.
He noticed that, when each number multiplied with some number other than
$1$
, they give some other result.
And the numbers when multiplied with
$1$
give the number back.
He explains his observation to the teacher who explains the concept of multiplicative identity to him.
Suppose multiplication of a number
$n$
with any other number gives the number back.
Then this number
$n$
, is known as the multiplicative identity.
$1$
is the only number, whose multiplication with any other number gives the number back.
Therefore, we get that
$1$
is the multiplicative identity.
Let’s understand one as multiplicative identity for whole numbers, integers and rational numbers.
Multiplication of one to whole number, will get us the same whole number back.
Multiplying a whole number
$2$
with multiplicative identity
$1$
, gives
$2$
as the result.
Now, suppose we have integer numbers
$5$
&
$−5$
, then multiplying them with
$1$
, gives the number back.
Therefore multiplication of one to integer, will give us the same Integer number back.
Similarly, on multiplying
$1$
with rational number
$2/3$
will give us the number
$2/3$
back.
Multiplication of one to rational number, will give us the same rational number back.
Revision
Suppose multiplication of a number
$n$
with any other number gives the number back.
Then this number
$n$
, is known as the multiplicative identity.
One is the multiplicative identity for whole numbers, Integer numbers and rational numbers.
The End