Question

Arrange the given fractions in descending order by making numerators equal: $\frac{5}{6},\frac{4}{15},\frac{8}{9}\text{and}\frac{1}{3}$

Answer 1

Step 1: Finding LCM of numerators 5, 4, 8 and 1:


Thus, the LCM of 5, 4, 8 and 1 is = $2\times 2\times 2\times 5=40$

Step 2: Bringing the fraction to same numerator as 40

By multiplying 8 in numerator and denominator in the $1^{\text{st}}$ fraction we get,

$\frac{5}{6}=\frac{5\times 8}{6\times 8}=\frac{40}{48}$

By multiplying 10 in numerator and denominator in the $2^{\text{nd}}$ fraction we get,

$\frac{4}{15}=\frac{4\times 10}{15\times 10}=\frac{40}{150}$

By multiplying 5 in numerator and denominator in the $3^{\text{rd}}$ fraction we get,

$\frac{8}{9}=\frac{8\times 5}{9\times 5}=\frac{40}{45}$

By multiplying 40 in numerator and denominator in the $4^{\text{th}}$ fraction we get,

$\frac{1}{3}=\frac{1\times 40}{3\times 40}=\frac{40}{120}$

Step 3: Comparing the fractions with equal numerators.
As denominators for the fractions are same, therefore, comparing the denominators of fractions we get,
$45<48<120<150$
$\therefore \frac{40}{45}>\frac{40}{48}>\frac{40}{120}<\frac{40}{150}$

$\therefore$ Descending order:

$\frac{8}{9}>\frac{5}{6}>\frac{1}{3}>\frac{4}{15}$