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______.

Complete Python Prime Pack

9 Courses     2 eBooks

Artificial Intelligence & Machine Learning Prime Pack

6 Courses     1 eBooks

Java Prime Pack

9 Courses     2 eBooks

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.

Updated on 10-Oct-2022 13:47:38