Question

Arrange the fractions given below in order from greatest to least (Descending order)

$4\frac{1}{7},1\frac{3}{21},1\frac{9}{14},2\frac{4}{7}$

Answer 1

The improper fraction of $4\frac{1}{7},1\frac{3}{21},1\frac{9}{14},2\frac{4}{7}$is

$$\begin{gathered} 4\frac{1}{7}=\frac{28+1}{7}=\frac{29}{7} \\ 1\frac{3}{21}=\frac{21+3}{21}=\frac{24}{21}=\frac{8}{7} \\ 1\frac{9}{14}=\frac{14+9}{14}=\frac{23}{14} \\ 2\frac{4}{7}=\frac{14+4}{7}=\frac{18}{7} \end{gathered}$$

Since, the denominator of given fraction are not same

The LCM of $7,14$ is $14$

Converting each of the given fractions into equivalent fraction with denominator as $14$

Consider $\frac{29}{7}\times 14=58$

On multiplying both numerator and denominator by $58$, we have

$\frac{29\times 58}{7\times 58}=\frac{58}{14}$

Consider $\frac{8}{7}\times 14=16$

On multiplying both numerator and denominator by $16$, we have

$\frac{8\times 16}{7\times 16}=\frac{16}{14}$

Consider $\frac{23}{14}\times 14=23$

On multiplying both numerator and denominator by $23$, we have

$\frac{23\times 23}{14\times 23}=\frac{23}{14}$

Consider $\frac{18}{7}\times 14=36$

On multiplying both numerator and denominator by $21$, we have

$\frac{18\times 36}{7\times 36}=\frac{36}{14}$

Hence, the like fractions of $\frac{29}{7},\frac{8}{7},\frac{23}{14},\frac{18}{7}$ is $\frac{58}{14},\frac{16}{14},\frac{23}{14},\frac{36}{14}$.

Now the denominator of given fraction not same

$\therefore$The descending order of $4\frac{1}{7},1\frac{3}{21},1\frac{9}{14},2\frac{4}{7}$is $\frac{58}{14},\frac{36}{14},\frac{23}{14},\frac{16}{14}$