Question

Arrange the given fractions in descending order of magnitude.

(iii) $\frac{5}{7},\frac{3}{8},\frac{9}{11}$

Answer 1

Step 1: Finding LCM of numerators of the given fractions

Given fractions are $\frac{5}{7},\frac{3}{8},\frac{9}{11}$

$\begin{array}{cc}3& 5,3,9\\ 3& 5,1,3\\ 5& 5,1,1\\ & 1,1,1\end{array}$

$\therefore \text{LCM of}3,5,9=3\times 3\times 5=45$

Step 2: Making the numerators of all the fractions same

$\Rightarrow \frac{5}{7}=\frac{5\times 9}{7\times 9}=\frac{45}{63}$

$\Rightarrow \frac{3}{8}=\frac{3\times 15}{8\times 15}=\frac{45}{120}$

$\Rightarrow \frac{9}{11}=\frac{9\times 5}{11\times 5}=\frac{45}{55}$

Step 3: Arranging all the fractions in descending order

When two or more fractions have same numerator, then the fraction having smaller denominator is greater and the fraction having greater denominator is smaller.

$\therefore \frac{45}{55}>\frac{45}{63}>\frac{45}{120}$

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

Hence, $\frac{9}{11}>\frac{5}{7}>\frac{3}{8}$ is the required descending order.