# The product of a rational number with its reciprocal is

\[

\left( a \right)0 \\

\left( b \right)1 \\

\left( c \right) - 1 \\

\left( d \right){\text{None of these}} \\

\]

Last updated date: 23rd Mar 2023

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Answer

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Hint: A rational number is a number that can be expressed as the quotient of fraction $\dfrac{p}{q}$ of two integers, a numerator p and a non-zero denominator q.

We know rational numbers can be expressed in the form of $\dfrac{p}{q}$ .

Rational number \[ = \dfrac{p}{q}.................\left( 1 \right)\]

Now, the reciprocal of $\dfrac{p}{q}$ is $\dfrac{q}{p}$ .

Reciprocal of rational number $ = \dfrac{q}{p}.................\left( 2 \right)$

Now the product of a rational number with its reciprocal,

Multiply (1) and (2) equations

$\left( {{\text{Rational number}}} \right) \times \left( {{\text{Reciprocal of rational number}}} \right) = \dfrac{p}{q} \times \dfrac{q}{p} = 1$

The product of a rational number with its reciprocal is 1.

So, the correct option is (b).

Note: Whenever we face such types of problems we use some important points. As we know, a rational number can be expressed in the form of $\dfrac{p}{q}$ and its reciprocal is $\dfrac{q}{p}$ . So, it is a proven product of rational numbers and its reciprocal always be 1.

We know rational numbers can be expressed in the form of $\dfrac{p}{q}$ .

Rational number \[ = \dfrac{p}{q}.................\left( 1 \right)\]

Now, the reciprocal of $\dfrac{p}{q}$ is $\dfrac{q}{p}$ .

Reciprocal of rational number $ = \dfrac{q}{p}.................\left( 2 \right)$

Now the product of a rational number with its reciprocal,

Multiply (1) and (2) equations

$\left( {{\text{Rational number}}} \right) \times \left( {{\text{Reciprocal of rational number}}} \right) = \dfrac{p}{q} \times \dfrac{q}{p} = 1$

The product of a rational number with its reciprocal is 1.

So, the correct option is (b).

Note: Whenever we face such types of problems we use some important points. As we know, a rational number can be expressed in the form of $\dfrac{p}{q}$ and its reciprocal is $\dfrac{q}{p}$ . So, it is a proven product of rational numbers and its reciprocal always be 1.

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