Consider the following statements :
A. The product of an integer and a rational number can never be a natural number
B. The quotient of division of an integer by a rational number can never be an integer
Which of the statements given above is/are correct ?

A only

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B only

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Both A and B

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Neither A nor B

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Solution

The correct option is D Neither A nor B
Let integer = 4 and Rational number = $\frac{2}{1}$
Then product = $4 \times \frac{2}{1} = 8$ (a natural number)
and Quotient = $4 \div \frac{2}{1} = 4 \times \frac{1}{2} = 2$ (an integer)

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Similar questions

Q. Which of the following statements is true?
(a) Product of two irrational numbers is always irrational
(b) Product of a rational and an irrational number is always irrational
(c) Sum of two irrational numbers can never be irrational
(d) Sum of an integer and a rational number can never be an integer

Consider the following three statements.
Statement – 1: Every natural number is a whole number
Statement – 2: Every rational number is an integer
Statement – 3: Every integer is a rational number.
Which of the following is true?

Q. In each of the following state if the statement is true (T) or false (F):
(i) The quotient of two integers is always an integer.
(ii) Every integer is a rational number.
(iii) Every rational number is an integer.
(iv) Every fraction is a rational number.
(v) Every rational number is a fraction
(vi) If

\frac{a}{b}

is a rational number and m any integer, then

\frac{a}{b} = \frac{a \times m}{b \times m}

(vii) Two rational numbers with different numerators cannot be equal.
(viii) 8 can be written as a rational number with any integer as denominator.
(ix) 8 can be written as a rational number with any integer as numerator.
(x)

\frac{2}{3} is equal to \frac{4}{6} .

Which one of the following is correct and which one is not correct? Give reasons.

1) If 'a' is a rational number and 'b' is irrational, then a+b is irrational.

2) The product of a non-profit rational number with an irrational number is always irrational.

3) Addition of any two irrational numbers can be rational.

4) Division of any two integers is an integer.

State whether the following statements are true or false:

(a) The set of all even natural numbers is a infinite set.

(b) Every non-empty subset of has the smallest element.

(d) For each rational number, one can find the next rational number.

(e)There is no largest rational number.

(f) Every integer is either even or odd.

(g) Between any two rational numbers, there is an integer.

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Consider the following statements : A. The product of an integer and a rational number can never be a natural number B. The quotient of division of an integer by a rational number can never be an integerWhich of the statements given above is/are correct ?

The correct option is D Neither A nor BLet integer = 4 and Rational number = 21Then product = 4×21=8 (a natural number)and Quotient = 4÷21=4×12=2 (an integer)

Consider the following statements :
A. The product of an integer and a rational number can never be a natural number
B. The quotient of division of an integer by a rational number can never be an integer
Which of the statements given above is/are correct ?

The correct option is D Neither A nor B
Let integer = 4 and Rational number = $\frac{2}{1}$
Then product = $4 \times \frac{2}{1} = 8$ (a natural number)
and Quotient = $4 \div \frac{2}{1} = 4 \times \frac{1}{2} = 2$ (an integer)