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Question

State whether the given statement is true of false:

(i) Zero is the smallest rational number.
(ii) Every integer is a rational number.
(iii) The quotient of two integers is always a rational number.
(iv) Every fraction is a rational number.
(v) Every rational number is a fraction.

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Solution

(i) False
For example,
1 is smaller than zero and is a rational number.
(ii)True
All integers can be written with the denominator 1.

(iii) False
Though 0 is an integer, when the denominator is 0, it is not a rational number.
For example, 10 is not a rational number.

(iv)True
(v) False
−1 is a rational number but not a fraction.

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