Question

The given rational numbers are $\frac{1}{2},\frac{4}{-5},\frac{-7}{8}$. If these numbers are arranged in the ascending order or descending order, then the middle number is

• A. $\frac{1}{2}$
• B. $\frac{-7}{8}$
• C. $\frac{4}{-5}$
• D. None

Answer 1

The correct option is C $(\frac{4}{-5})$

Let given numbers arranged in the descending order.
Since positive value is always greater than the negative value.
So, $\frac{1}{2}$ would be the first element in the arrangement.
Now consider , the negative fractions $\frac{-4}{5}$ and $\frac{-7}{8}$
Before we compare them, lets make their denominators equal as
$\frac{-4}{5}\times \frac{8}{8}=-\frac{32}{40}$ and $\frac{-7}{8}\times \frac{5}{5}=-\frac{35}{40}$
Since $-32>-35$
Dividing $40$ on both sides of inequality
$\Rightarrow -\frac{32}{40}>-\frac{35}{40}$
$\therefore -\frac{4}{5}>-\frac{7}{8}$
The descending order is $\frac{1}{2}>\frac{-4}{5}>\frac{-7}{8}$

Also, the ascending order is $\frac{-7}{8}<\frac{-4}{5}<\frac{1}{2}$
So, middle number is $\frac{-4}{5}$.