Question

Arrange the given fractions in ascending order of their magnitude $:$ $\frac{2}{7}$ ‚ $\frac{5}{6}$ ‚ $\frac{3}{8}$ and $\frac{4}{9}$

Answer 1

Step 1:Convert all the fractions into like fractions by taking out the L $.$C $.$M of all the denominators

Given fractions are $\frac{2}{7}$ ‚ $\frac{5}{6}$ ‚ $\frac{3}{8}$ and $\frac{4}{9}$

Denominators are $7$‚ $6$ ‚$8$ and $9$

L $.$C $.$M of $7$‚ $6$ ‚$8$ and $9$ is $504$

$\frac{2}{7}$ $=$ $\frac{2\times 72}{7\times 72}$ $=$$\frac{144}{504}$

$\frac{5}{6}$ $=$ $\frac{5\times 84}{6\times 84}$ $=$$\frac{420}{504}$

$\frac{3}{8}$ $=$ $\frac{3\times 63}{8\times 63}$ $=$$\frac{189}{504}$

$\frac{4}{9}$ $=$ $\frac{4\times 56}{9\times 56}$ $=$$\frac{224}{504}$

Step 2: Arrange all the numerators in such a way that smallest will be the first‚ then second smallest ‚ then third smallest and finally the largest numerator

$144<189$$<224$$<420$

Hence ‚ $\frac{2}{7}$ $<$$\frac{3}{8}$ $<$ $\frac{4}{9}$$<$$\frac{5}{6}$