Q-1: Is zero a rational number? Can you write in the form $\cfrac{p}{q}$, where $p$ and $q$ are integers and $q\ne0$.
Solution:
Yes, zero is a rational number.
zero can be represented as $\cfrac{0}{1}, \cfrac{0}{2}…$ etc which is of the form $\cfrac{p}{q}$ where $q\ne0$.
Q-2: Find six rational numbers between 3 and 4.
Solution:
In order to find 6 rational numbers between 3 and 4, we will multiply 3 and 4 by $\cfrac{7}{7}$, we get,
$3 =3\times\cfrac{7}{7} = \cfrac{21}{7}$
$4 =4\times\cfrac{7}{7} = \cfrac{28}{7}$
$\therefore$ Six rational numbers between 3 and 4 are $\cfrac{22}{7},\cfrac{23}{7},\cfrac{24}{7},\cfrac{24}{7},\cfrac{25}{7},\cfrac{26}{7}$.
Q-3: Find five rational numbers between $\cfrac{3}{5}$ and $\cfrac{4}{5}$.
Solution:
In order to find 5 rational numbers between $\cfrac{3}{5}$ and $\cfrac{4}{5}$, we will multiply $\cfrac{3}{5}$ and $\cfrac{4}{5}$ by $\cfrac{6}{6}$, we get,
$\cfrac{3}{5} =\cfrac{3}{5}\times\cfrac{6}{6} = \cfrac{18}{30}$
$\cfrac{4}{5} =\cfrac{4}{5}\times\cfrac{6}{6} = \cfrac{24}{30}$
$\therefore$ Five rational numbers between $\cfrac{3}{5}$ and $\cfrac{4}{5}$ are $\cfrac{19}{30},\cfrac{20}{30},\cfrac{21}{30},\cfrac{22}{30},\cfrac{23}{30}$.
Q-4: State whether the following statements are true or false. Give reasons for your answers.
(i). Every natural number is a whole number.
(ii). Every integer is a whole number.
(iii). Every rational number is a whole number.
Solution:
(i). True
Zero and Natural numbers together form whole numbers. Therefore, every natural number is a whole number.
(ii). False
Negative numbers like -3,-2 etc are integers, but they are not whole numbers.
(iii). False
Rational numbers like $\cfrac{2}{3},\cfrac{1}{2}$ etc are not whole numbers.
