Question

(a) Find wether the following numbers are equal or greater or less than $\frac{19}{26}$. The numbers are $\frac{247}{338}$, $\frac{19}{21}$ and $\frac{26}{32}$.

(b) Find a rational number which lies between $\frac{1}{2}$ and $\frac{1}{4}$.
[3 MARKS]

Answer 1

(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) A rational number which lies between $\frac{1}{2}$ and $\frac{1}{4}$ is:

$\Rightarrow \frac{\frac{1}{2}+\frac{1}{4}}{2}$

$\Rightarrow \frac{\frac{3}{4}}{2}$

$\Rightarrow \frac{3}{8}$