Question

Arrange the given fractions in descending order of their magnitude $:$ $\frac{5}{12}$ ‚ $\frac{3}{5}$ ‚ $\frac{2}{3}$ and $\frac{4}{15}$

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 $\frac{5}{12}$ ‚ $\frac{3}{5}$ ‚ $\frac{2}{3}$ and $\frac{4}{15}$

Denominators are $12$‚ $5$ ‚$3$ and $15$

L $.$C $.$M of $12$‚ $5$ ‚$3$ and $15$ is $60$

$\frac{5}{12}$ $=$ $\frac{5\times 5}{12\times 5}$ $=$$\frac{25}{60}$

$\frac{3}{5}$ $=$ $\frac{3\times 12}{5\times 12}$ $=$$\frac{36}{60}$

$\frac{2}{3}$ $=$ $\frac{2\times 20}{3\times 20}$ $=$$\frac{40}{60}$

$\frac{4}{15}$ $=$ $\frac{4\times 4}{15\times 4}$ $=$$\frac{16}{60}$

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

$40>36$$>25$$>16$

Hence ‚ $\frac{2}{3}$ $>$$\frac{3}{5}$ $>$ $\frac{5}{12}$$>$$\frac{4}{15}$