Question

Arrange the following rational numbers in descending order.

$\frac{-3}{4},\frac{2}{11},\frac{3}{5},-4$

Answer 1

Step 1: Convert the given rational numbers into equivalent rational numbers.

Given: $\frac{-3}{4},\frac{2}{11},\frac{3}{5},-4$

These rational numbers are not equivalent, so first convert them into equivalent rational numbers.

Take LCM of the denominators of given rational numbers.

LCM of $4,11\text{and}5\mathrm{is}220$.

Now, Multiply the numerator and denominator of the given rational numbers with the same number such that the denominators become $220$.

$$\begin{gathered} \frac{-3}{4}=\frac{-3\times 55}{4\times 55}=\frac{-165}{220} \\ \frac{2}{11}=\frac{2\times 20}{11\times 20}=\frac{40}{220} \\ \frac{3}{5}=\frac{3\times 44}{5\times 44}=\frac{132}{220} \\ -4=\frac{-4\times 220}{1\times 220}=\frac{-880}{220} \end{gathered}$$

Step 2: Arrange the given numbers in descending order.

We know that the fractions with the greater numerator are greater.

So, $\frac{132}{220}>\frac{40}{220}>\frac{-165}{220}>\frac{-880}{220}$.

Hence, numbers arranged in descending order are $\frac{3}{5}>\frac{2}{11}>\frac{-3}{4}>-4$.