Answer:
:
(a) Answer: 2 Marks
(b) Answer: 1 Mark
(a) When we multiply by 13 in denominator and the numerator of$\frac{19}{26}$ we get $\frac{247}{338}$, therefore$\frac{19}{26}=\frac{247}{338}$.
By inspection, when the numerator is same and the denominator is different then the fraction having a large value of denominator is smaller than the fraction having less value of denominator.
Hence, $\frac{19}{26}$ < $\frac{19}{21}$.
For comparing $\frac{19}{26}$ and $\frac{13}{16}$ we have to make the denominator of both the fraction by taking LCM of 26 and 16 = 416.
$\frac{(19\times 16)}{(26\times 16)}=\frac{304}{416}$, $\frac{(13\times 26)}{(16\times 26)}=\frac{338}{416}$
338>304. Hence, $\frac{26}{32}$ >$\frac{19}{26}$.
(b) Arational number which lies between $\frac{1}{2}$ and$\frac{1}{4}$ is:
$\Rightarrow \frac{\frac{1}{2}+\frac{1}{4}}{2}$
$\Rightarrow \frac{\frac{3}{4}}{2}$
$\Rightarrow \frac{3}{8}$