Fill in the blanks.
(i) Zero has_____ reciprocal.
(ii) The numbers_____ and____ are their own reciprocals.
(iii) The reciprocal of $ -5 $ is____.
(iv) Reciprocal of $ \frac{1}{x} $, where $ x
≠ 0 $ is____.
(v) The product of two rational numbers is always a________.
(vi) The reciprocal of a positive rational number is______.

To do:

We have to fill in the given blanks.

Solution:

(i) Zero has no reciprocal.

Any number divided by zero is not defined. Therefore, zero has no reciprocal.

(ii) The numbers $1$ and $-1$ are their own reciprocals.

Reciprocal of $a$ is $\frac{1}{a}$.

This implies,

Reciprocal of $1$ is $\frac{1}{1}=1$.

Reciprocal of $-1$ is $\frac{1}{-1}=-1$.

(iii) The reciprocal of \( -5 \) is $-\frac{1}{5}$

Reciprocal of $a$ is $\frac{1}{a}$.

Reciprocal of $-5$ is $\frac{1}{-5}=-\frac{1}{5}$.

(iv) Reciprocal \( \frac{1}{x} \), where \( x ≠ 0 \) is $x$.

Reciprocal of $a$ is $\frac{1}{a}$.

This implies,

Reciprocal \( \frac{1}{a} \), where \( a ≠ 0 \) is $a$

(v) The product of two rational numbers is always a rational number.

For example,

$\frac{1}{3}\times\frac{2}{5}=\frac{1\times2}{3\times5}$

$=\frac{2}{15}$

Here, $\frac{1}{3}, \frac{2}{5}$ and $\frac{2}{15}$ are rational numbers.

(vi) The reciprocal of a positive rational number is positive.

For example,

The reciprocal of $5$ is $\frac{1}{5}$

Here, $5$ and $\frac{1}{5}$ are both positive.

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Updated on: 10-Oct-2022

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