Question

Arrange the given fractions in descending order by making numerators equal:
$\left(ii\right)$$\frac{3}{7},\frac{4}{9},\frac{5}{7}$ and $\frac{8}{11}$

Answer 1

Finding $LCM$ of numerators of fractions $3,4,5$ and $8:$

$\begin{array}{cc}2\mid & 3,4,5,8\\ 2\mid & 3,2,5,4\\ 2\mid & 3,1,5,2\\ 3\mid & 3,1,5,1\\ 5\mid & 1,1,5,1\\ \mid & 1,1,1,1\end{array}$

Thus, the $LCM$ of $3,4,5$ and $8$ is $2\times 2\times 2\times 3\times 5=120$

Bringing the fractions to same numerator as $120$

By multiplying $40$ in numerator and denominator in the $1^{st}$ fraction we get,

$\frac{3}{7}=\frac{3\times 40}{7\times 40}=\frac{120}{280}$

By multiplying $30$ in numerator and denominator in the $2^{nd}$ fraction we get,

$\frac{4}{9}=\frac{4\times 30}{9\times 30}=\frac{120}{270}$

By multiplying $24$ in numerator and denominator in the $3^{rd}$ fraction we get,

$\frac{5}{7}=\frac{5\times 24}{7\times 24}=\frac{120}{168}$

By multiplying $15$ in numerator and denominator in the $4^{th}$ fraction we get,

$\frac{8}{11}=\frac{8\times 15}{11\times 15}=\frac{120}{165}$

Comparing the fractions with equal numerators

As numerators for the fractions are same, therefore, comparing the denominators of fractions we get,

$165<168<270<280$

$\therefore \frac{120}{165}>\frac{120}{168}>\frac{120}{270}>\frac{120}{280}$

$\therefore$ Descending order:

$\frac{8}{11}>\frac{5}{7}>\frac{4}{9}>\frac{3}{7}$