Question

In a rational number of the form p/q,q must be a non zero integer.True or false ​

Answer 1

Answer:

TRUE

Explanation:

Yes, if a rational number is in the form p/q, then q should not be equal to 0.

Why so?

Division by zero is not valid/allowed. We can't predict if a number is divided by 0, what would be the quotient.

Let us suppose, 1 is divided by zero and the question is a

1/0 = a

1 = a × 0

1 = 0 !

which is not possible.

As 0 × a will never be any number except 0.

So, q should be non zero integer.

NOTE: p could be any integer including 0. It will give the answer as 0 and 0 is a rational number.

0/1 = 0/2 = 0/3 = 0

Answer 2

$\huge\bold{\mathbb{QUESTION}}$

In a rational number of the form ${\dfrac{p}{q}},$ $\,q$ must be a non-zero integer.

True or False

$\huge\bold{\mathbb{TO\:FIND}}$

Whether the given statement is true or false.

$\huge\bold{\mathbb{ANSWER}}$

True

$\huge\bold{\mathbb{EXPLANATION}}$

In a rational number of the form ${\dfrac{p}{q}},$ $\,q$ must be a non-zero integer.

Because division by $0$ is not possible or is undefined. We can't find the quotient on dividing any number by $0.$

For example, ${\dfrac{x}{0}}$ is undefined.

$\:\:\:\:\:\;\;$ Here, $x$ is a non-zero integer.

To understand clearly, let's divide $2$ by $0$ and take the quotient as $x.$

So, ${\dfrac{2}{0}}=x.$

Here,

• $2$ is the dividend.

• $0$ is the divisor.

• $x$ is the quotient.

We know that:

$\;\;\;\;\;\;\;\; \boxed{\boxed{\sf Dividend=Quotient\times Divisor}}$

$\sf Quotient\times Divisor$

$=x\times0$

$=0$ $\;\;\; \small{\{\sf Any\:number\times 0=0\}}$

But, $2\neq 0$

$\therefore \sf Dividend\neq Quotient\times Divisor$

So, the division is not possible.

$\huge\bold{\mathbb{EXPLORE\:MORE}}$

• Division is the distribution of something into a number of equal parts. For example, a cake is divided into $4$ equal parts.

• It is the opposite of multiplication.

• Division has $4$ parts, namely dividend, divisor, quotient and remainder.