Mathematics
State whether the given statement is true or false :
(i) The quotient of two integers is always a rational number.
(ii) Every rational number is a fraction.
(iii) Zero is the smallest rational number.
(iv) Every fraction is a rational number.
Rational Numbers
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Answer
(i) False
Reason — While a rational number is defined as the quotient of two integers , the denominator q cannot be zero. If the divisor (the second integer) is zero, the quotient is undefined and is not a rational number.
(ii) False
Reason — Fractions typically refer to a part of a whole and are usually represented as a ratio of two natural numbers. Rational numbers include negative values (like ) and integers (like -5), which are not traditionally considered fractions in their standard form.
(iii) False
Reason — Rational numbers include negative values. Therefore, any negative rational number (such as -1 or ) is smaller than zero. Because the set of rational numbers extends infinitely in the negative direction, there is no "smallest" rational number.
(iv) True
Reason — A fraction is represented as where a and b are whole numbers and b ≠ 0. Since whole numbers are also integers, every fraction fits the definition of a rational number.
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