Question

Arrange the following in descending order:

$\frac{-7}{9},\frac{2}{-3},\frac{5}{6}$

Answer 1

Step 1: Converting given fraction into equivalent fractions.

To convert them in equivalent fraction we have to make $\frac{2}{-3}$ in standard form.

$\frac{2}{-3}=\frac{-2}{3}$ (Multiplying numerator and denominator by $-1$)

LCM of $9,3$ and $6$ is $18$.

Now convert the given rational numbers in equivalent fraction with denominator $18$.

$$\begin{gathered} \frac{-7\times 2}{9\times 2}=\frac{-14}{18}, \\ \frac{-2\times 6}{3\times 6}=\frac{-12}{18} \end{gathered}$$

and $\frac{5\times 3}{6\times 3}=\frac{15}{18}$

Step 2: Arranging fractions in descending order.

Descending order means to arrange numbers in decreasing order, that is, from largest to smallest.

We know that fractions with smaller numerators are smaller and vice-versa.

Here, $15>-12>-14$

So, $\frac{15}{18}>\frac{-12}{18}>\frac{-14}{18}$..

Hence, arrangement of given fractions in descending order is $\frac{5}{6}>\frac{-2}{3}>\frac{-7}{9}$.