Question

The rational number which is not lying between $\frac{5}{16}$ and $\frac{1}{2}$ is
$\left(a\right)\frac{3}{8}$

$\left(b\right)\frac{7}{16}$

$\left(c\right)\frac{1}{4}$

$\left(d\right)\frac{13}{32}$

Answer 1

Given fractions are $\frac{5}{16}$ and $\frac{1}{2}$

Lets convert the given fractions into like fractions,

Here, LCM of denominators $16$, $2$ is $16$. [$\because$ $16$ is multiple of $2$]

$\Rightarrow$ $\frac{1}{2}$ $\times$ $\frac{16}{16}$ $=\frac{8}{16}$

i.e., given fractions are in the form of like fractions $\frac{5}{16}$ and $\frac{8}{16}$

Now, lets check the options,

$\left(a\right)$ $\frac{3}{8}=\frac{3}{8}\times \frac{2}{2}=\frac{6}{16}$ lie between $\frac{5}{16}$ and $\frac{8}{16}$

$\left(b\right)$ $\frac{7}{16}$ lie between $\frac{5}{16}$ and $\frac{8}{16}$

$\left(c\right)$ $\frac{1}{4}=\frac{1}{4}\times \frac{4}{4}=\frac{4}{16}$ doesn't lie between $\frac{5}{16}$ and $\frac{8}{16}$

$\left(d\right)$ $\frac{13}{32}=\frac{13}{32}$ $÷$ $\frac{2}{2}=\frac{6.5}{16}$ lie between $\frac{5}{16}$ and $\frac{8}{16}$.

Hence, Option $\left(c\right)$ is correct.