Answer:
:
a) Each rational number: 0.5 Marks
b) Each operation: 0.5 Marks
(a) There are infinite numbers of rational numbers that lie between two points on a number line.
Consider the rational numbers $\frac{2}{5}$ and$\frac{6}{5}$.
Take the average of two numbers $\frac{2+6}{5\times 2}$ = $\frac{8}{10}$
$\frac{8}{10}$ lies in the middle of $\frac{2}{5}$and $\frac{6}{5}$.
Now take the average of$\frac{2}{5}$ and $\frac{8}{10}$. It is $(\frac{2}{5}+\frac{8}{10})\times \frac{1}{2}$= $\frac{4+8}{10}\times \frac{1}{2}$= $\frac{12}{20}$
So, as we proceed in this, we will get an infinite number of rational number between two points.
(b) (i) $x+y=\frac{1}{10}+\frac{-3}{8}$
$\Rightarrow \frac{1}{10}-\frac{3}{8}=\frac{8-30}{80}$
$\Rightarrow \frac{-22}{80}=\frac{-11}{40}$
(ii) $x-y=\frac{1}{10}-\frac{-3}{8}$
$\Rightarrow \frac{1}{10}+\frac{3}{8}=\frac{8+30}{80}$
$\Rightarrow \frac{38}{80}=\frac{19}{40}$
(iii) $x\times y=\frac{1}{10}\times \frac{-3}{8}=\frac{-3}{80}$
(iv) $x÷y=\frac{1}{10}÷\frac{-3}{8}$
$\Rightarrow \frac{1}{10}\times \frac{8}{-3}=\frac{8}{-30}$
$\Rightarrow \frac{-8}{30}=\frac{-4}{15}$