Question

Arrange the fractions $\frac{3}{5},\frac{2}{3},\frac{6}{7},\frac{5}{8}$ in descending order

Answer 1

We have to arrange $\frac{3}{5},\frac{2}{3},\frac{6}{7},\frac{5}{8}$ in Descending order :

Step 1 Making the denominator same by taking LCM of denominators of fractions :

LCM of $5,3,7,8$ $=5\times 3\times 7\times 8=840$

Step 2 Making equivalent fractions of given fractions whose denominator is $840$ :

$$\begin{gathered} \frac{3}{5}=\frac{3\times 168}{5\times 168}=\frac{504}{840} \\ \frac{2}{3}=\frac{2\times 280}{3\times 280}=\frac{560}{840} \\ \frac{6}{7}=\frac{6\times 120}{7\times 120}=\frac{720}{840} \\ \frac{5}{8}=\frac{5\times 105}{8\times 105}=\frac{525}{840} \end{gathered}$$

Step 3 Arrange the equivalent fractions obtained in step 2 in descending order by comparing their numerators :

Descending order : $\frac{720}{840},\frac{560}{840},\frac{525}{840},\frac{504}{840}$ $\Rightarrow \frac{6}{7},\frac{2}{3},\frac{5}{8},\frac{3}{5}$

Hence Descending order of $\frac{3}{5},\frac{2}{3},\frac{6}{7},\frac{5}{8}$ is $\frac{6}{7},\frac{2}{3},\frac{5}{8},\frac{3}{5}$