Question

Arrange the following numbers in descending order.
$-2,\frac{4}{-5},\frac{-11}{20},\frac{3}{4}$

• A. $\frac{3}{4}>-2>\frac{-11}{20}>\frac{4}{-5}$
• B. $\frac{3}{4}>\frac{-11}{20}>\frac{4}{-5}>-2$
• C. $\frac{3}{4}>\frac{4}{-5}>-2>\frac{-11}{20}$
• D. $\frac{3}{4}>\frac{4}{-5}>\frac{-11}{20}>-2$

Answer 1

The correct option is B $\frac{3}{4}>\frac{-11}{20}>\frac{4}{-5}>-2$

The rational number $\frac{4}{-5}$ is same as $\frac{-4}{5}$.

Now consider the given rational numbers $-2,\frac{-11}{20},\frac{-4}{5}$ and $\frac{3}{4}$ and make their denominator same by taking the LCM of the denominators as follows:

LCM$(5,20,4)=20$

The given fractions now with denominator $20$ can be written as:

$\frac{-2\times 20}{1\times 20}=\frac{-40}{20}\frac{-4\times 4}{5\times 4}=\frac{-16}{20}\frac{-11\times 1}{20\times 1}=\frac{-11}{20}\frac{3\times 5}{4\times 5}=\frac{15}{20}$

The descending order of the rational numbers is:

$\frac{15}{20}>\frac{-11}{20}>\frac{-16}{20}>\frac{-40}{20}\Rightarrow \frac{3}{4}>\frac{-11}{20}>\frac{4}{-5}>-2$

Hence, the descending order is $\frac{3}{4}>\frac{-11}{20}>\frac{4}{-5}>-2$.