Question

Arrange the following in descending order:

$\frac{-25}{6},\frac{-15}{-4},\frac{53}{12},\frac{-17}{4}$

Answer 1

Step 1: Converting given fraction into equivalent fractions.

To convert them in equivalent fraction we have to make $\frac{-15}{-4}$ in standard form.

$\frac{-15}{-4}=\frac{15}{4}$ (Minus sign gets cancelled)

LCM of $6,4$ and $12$ is $12$.

Now convert the given rational numbers in equivalent fraction with denominator $12$.

$$\begin{gathered} \frac{-25\times 2}{6\times 2}=\frac{-50}{12}, \\ \frac{15\times 3}{4\times 3}=\frac{75}{12}, \\ \frac{53\times 1}{12\times 1}=\frac{53}{12} \end{gathered}$$

and $\frac{-17\times 3}{4\times 3}=\frac{-51}{12}$

Step 2: Arranging the numbers in descending order.

Descending order means to arrange numbers in decreasing order, that is, from largest to smallest and we know that fractions with smaller numerators are smaller and vice-versa.

Here, $75>53>-50>-51$

so, $\frac{75}{12}>\frac{53}{12}>\frac{-50}{12}>\frac{-51}{12}$.

Hence, the arrangement of given fractions in descending order is $\frac{15}{4}>\frac{53}{12}>\frac{-25}{6}>\frac{-17}{4}$.