Question

What is the multiplicative and additive identity of Rational Numbers?

Answer 1

Answer :

Additive identity of rational number : Additive identity is a number that gives same rational number after that identity add into any rational number .

Let rational number = x
And
Additive identity = y

So from our basic definition , we get

x + y = x

So,

y = 0

So, we can say that additive identity of rational numbers is Zero .

we can check for any rational number , As we know rational numbers can be expressed in form of $\frac{p}{q}$ , where q $\ne$ 0 ,
so,

$\frac{1}{2}$ + additive identity = $\frac{1}{2}$ , And as we now know additive identity = 0 ,

So,

$\frac{1}{2}$ + 0 = $\frac{1}{2}$

$\frac{1}{2}$ = $\frac{1}{2}$ ( Verified )

multiplicative identity for rational numbers : multiplicative identity is a number that gives same rational number after that identity multiplied into any rational number .

Let rational number = x
And
multiplicative identity = y

So from our basic definition , we get

xy = x

So,

y = 1

So, we can say that multiplicative identity of rational numbers is One .

we can check for any rational number , As we know rational numbers can be expressed in form of $\frac{p}{q}$ , where q $\ne$ 0 ,
so,

$\frac{1}{2}$( multiplicative identity ) = $\frac{1}{2}$ , And as we now know multiplicative identity = 1 ,

So,

$\frac{1}{2}$ ( 1 ) = $\frac{1}{2}$

$\frac{1}{2}$ = $\frac{1}{2}$ ( Verified )