Question

Arrange the following in ascending order:

(i) $\frac{2}{7},\frac{3}{5},\frac{5}{6}$

(ii) $\frac{1}{5},\frac{3}{7},\frac{7}{10},\frac{1}{6}$

Answer 1

(i) we have $\frac{2}{7},\frac{3}{5}$ and $\frac{5}{6}$

LCM of 7, 5 and 6 = 210

$\therefore \frac{2}{7}\times \frac{30}{30}=\frac{60}{210}$

$\frac{3}{5}\times \frac{42}{42}=\frac{126}{210}$

$\frac{5}{6}\times \frac{35}{35}=\frac{175}{210}$

Since, the denominators are same.

$\therefore 175>126>60$

Hence, the required order is

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

(ii) we have $\frac{1}{5},\frac{3}{7},\frac{7}{10}$ and $\frac{1}{6}$

LCM of 5, 7, 10 and 6 =210

$\frac{1}{5}\times \frac{42}{42}=\frac{42}{210}$

$\frac{3}{7}\times \frac{30}{30}=\frac{90}{210}$

$\frac{7}{10}\times \frac{21}{21}=\frac{147}{210}$

$\frac{1}{6}\times \frac{35}{35}=\frac{35}{210}$

Since, the denominator are same.

$\therefore 147>90>42>35$

Hence, the required order is $\frac{7}{10}>\frac{3}{7}>\frac{1}{5}>\frac{1}{6}.$