Question

Arrange the following fractions in increasing order $:$

$\frac{1}{2},\frac{3}{2},\frac{1}{5},\frac{2}{7},\frac{1}{14}$

Answer 1

Step 1 We find the L.C.M. of the denominators of the fractions to make the denominators same.

L.C.M. of $2,5,7,14$ = $140$

Step 2 To make the fraction as like fractions

Divide the L.C.M. by the denominator of fractions, then multiply both the numerator and denominator of fraction with the number get after dividing L.C.M

As in fraction $\frac{1}{2}$ denominator is $2$

Divide $140$ $÷$ $2$ $=$$70$

Now, multiply both numerator and denominator by $70$, $\frac{1}{2}\times \frac{70}{70}=\frac{70}{140}$

Similarly,$\frac{3}{2}$$=$$\frac{3}{2}\times \frac{70}{70}=\frac{210}{140}$ because $140$ $÷$ $2$ $=$$70$

$\frac{1}{5}=\frac{1}{5}\times \frac{28}{28}=\frac{28}{140}$ because $140÷5=28$

$\frac{2}{7}=\frac{2}{7}\times \frac{20}{20}=\frac{40}{140}$ because $140÷7=20$

$\frac{1}{14}=\frac{1}{14}\times \frac{10}{10}=\frac{10}{140}$because $140÷14=10$

Step 3 Compare the like fractions

$\frac{70}{140},\frac{210}{140},\frac{28}{140},\frac{40}{140},\frac{10}{140}$

Comparing numerators , we find $210>70>40>28>10$

so $\frac{210}{140}>\frac{70}{140}>\frac{40}{140}>\frac{28}{140}>\frac{10}{140}$

so $\frac{3}{2}>\frac{1}{2}>\frac{2}{7}>\frac{1}{5}>\frac{1}{14}$

Therefore, fractions in increasing order $\frac{1}{14}<\frac{1}{5}<\frac{2}{7}<\frac{1}{2}<\frac{3}{2}$