Question

Arrange the following fractions in descending order.

• A. $\frac{2}{5}$
• B. $\frac{7}{4}$
• C. $\frac{2}{5}\times \frac{7}{4}$
• D. $2$

Answer 1

We need to arrange $\frac{2}{5},\frac{7}{4}$ and $\frac{2}{5}\times \frac{7}{4}$ in decreasing order.

By making the fractions as like fractions, we get

$\frac{2}{5}=\frac{2}{5}\times \frac{4}{4}=\frac{8}{20}\cdots \left(1\right)$
$\frac{7}{4}=\frac{7}{4}\times \frac{5}{5}=\frac{35}{20}\cdots \left(2\right)$
$\frac{2}{5}\times \frac{7}{4}=\frac{14}{20}\cdots \left(3\right)$
[Making same denominator as LCM of (5, 4, 10)=20]

From $\left(1\right),\left(2\right),\left(3\right)$, it is clear that
$\frac{35}{20}>\frac{14}{20}>\frac{8}{20}$
$\Rightarrow \frac{7}{4}>\frac{2}{5}\times \frac{7}{4}>\frac{2}{5}$

Hence, $\frac{7}{4},\frac{2}{5}\times \frac{7}{4}$ and $\frac{2}{5}$ are in descending order.