Question

(1) Write all the rational numbers obtained by using each of the integers −4, 3 and 1 once.

(2) Are the following statements true or false?
(i) The number $\frac{8}{-7}$is conventionally written as $\frac{-8}{7}$.
(ii) 0 is the smallest natural number.
(iii) −4 is a whole number.

Answer 1

(1) Any number which can be expressed in the form of $\frac{p}{q}$, where p and q are integers and $q\ne 0$, is called a rational number.
So, the rational numbers formed using the digits – 4, 3, and 1 are $\frac{-4}{3},\frac{-4}{1},\frac{-4}{-4},\frac{-3}{4},\frac{3}{1},\frac{-3}{-3},\frac{-1}{4},\frac{1}{3},\frac{1}{1}$.

(2)
(i) The given statement is true.
(ii) The given statement is false because natural numbers are the counting numbers starting from 1: 1, 2, 3, …
So, 1 is the smallest natural number.
(iii) The given statement is false because whole numbers are the counting numbers starting from 0: 0, 1, 2, 3, …
Negative numbers are not whole numbers.