Question

Arrange the given fractions in descending order by making denominators equal: $\frac{1}{10},\frac{6}{11},\frac{8}{11}\text{and}\frac{3}{5}$

Answer 1

Step 1: Finding LCM of denominators 1, 6, 8 and 3:

Thus, the LCM of 1, 6, 8 and 3 is $2\times 2\times 2\times 3=24$

Step 2: Bringing the fraction to same numerator as 24

By multiplying 24 in numerator and denominator in the $1^{\text{st}}$ fraction we get,

$\frac{1}{10}=\frac{1\times 24}{10\times 24}=\frac{24}{240}$

By multiplying 4 in numerator and denominator in the $2^{\text{nd}}$ fraction we get,

$\frac{6}{11}=\frac{6\times 4}{11\times 4}=\frac{24}{44}$

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

$\frac{8}{11}=\frac{8\times 3}{11\times 3}=\frac{24}{33}$

By multiplying 8 in numerator and denominator in the $4^{\text{th}}$ fraction we get,

$\frac{3}{5}=\frac{3\times 8}{5\times 8}=\frac{24}{40}$

Step 2: Comparing the fractions with equal numerators.
As numerators for the fractions are same, comparing the denominators fractions we get,
$33<40<44<240$
$\therefore \frac{24}{33}>\frac{24}{40}>\frac{24}{44}>\frac{24}{240}$

$\therefore$ Descending order:

$\frac{8}{11}>\frac{3}{5}>\frac{6}{11}>\frac{1}{10}$