Question

Arrange the fractions in descending order

$\frac{2}{6},\frac{5}{3},\frac{3}{4},\frac{2}{7}$

• A. $\frac{5}{3},\frac{3}{4},\frac{2}{6},\frac{2}{7}$
• B. $\frac{5}{3},\frac{3}{4},\frac{2}{7},\frac{2}{6}$
• C. $\frac{3}{4},\frac{5}{3},\frac{2}{6},\frac{2}{7}$
• D. $\frac{5}{3},\frac{2}{6},\frac{3}{4},\frac{2}{7}$

Answer 1

The correct option is

A

$\frac{5}{3},\frac{3}{4},\frac{2}{6},\frac{2}{7}$

In order to compare the given fractions, we must make their denominators same.

So, the LCM of the denominators is $6\times 3\times 4\times 7=84$

Converting all the fractions into fractions with common base, $84,$ we get the fractions as:

$\frac{2}{6}\times \frac{14}{14}=\frac{28}{84}$

$\frac{5}{3}\times \frac{28}{28}=\frac{140}{84}$

$\frac{3}{4}\times \frac{21}{21}=\frac{63}{84}$

$\frac{2}{7}\times \frac{12}{12}=\frac{24}{84}$

Now, since, the denominators of the fractions are same, we can compare the fractions by comparing their numerators.

Arranging these in descending order we get, $\frac{140}{84}>\frac{63}{84}>\frac{28}{84}>\frac{24}{84}$.

Correspondingly arranging the original fractions in descending order, we get

$\Rightarrow \frac{5}{3}>\frac{3}{4}>\frac{2}{6}>\frac{2}{7}$