Question

If all the rational numbers $\frac{3}{7},\frac{1}{14},\frac{4}{7},\frac{2}{7},\frac{5}{7}$ and $\frac{5}{14}$ are arranged in descending order of their values which one will be the third?

• A. $\frac{1}{14}$
• B. $\frac{3}{7}$
• C. $\frac{5}{14}$
• D. $\frac{8}{14}$

Answer 1

The correct option is C $\frac{5}{14}$

The LCM of the denominators $7,14$ is $14$. Therefore, the given numbers will be:

$\frac{3\times 2}{7\times 2}=\frac{6}{14}\frac{4\times 2}{7\times 2}=\frac{8}{14}\frac{2\times 2}{7\times 2}=\frac{4}{14}\frac{5\times 2}{7\times 2}=\frac{10}{14}$

Thus, the numbers in ascending order are shown below:

$\frac{1}{14}$ ,$\frac{4}{14}$ ,$\frac{5}{14}$ ,$\frac{6}{14}$, $\frac{8}{14}$,$\frac{10}{14}$

So, in simplified form

$\frac{1}{14}$ ,$\frac{2}{7}$ ,$\frac{5}{14}$ ,$\frac{3}{7}$, $\frac{4}{7}$,$\frac{5}{7}$

$\frac{5}{14}$ is in third position.