### Theory:

Let's see a situation before we get into the Unlike fraction.

At a birthday party, everyone dressed in different colors of costumes. Which made the birthday party so colorful. Here the different people wore different colors.

Similar to the above event, unlike fractions are fractions with different denominators.
Unlike fractions are fractions with different denominators.
Example:
$\frac{4}{5},\frac{2}{3},\frac{6}{7},\frac{24}{10},\frac{45}{15}$

Here the denominators of all the fractions are different, hence it is a, Unlike fractions.
Let us see how we can order the unlike fractions with the same numerator and compare the unlike fractions with different denominator.
Ordering of unlike fractions with the same numerator:
$\frac{6}{13},\phantom{\rule{0.147em}{0ex}}\frac{6}{14},\phantom{\rule{0.147em}{0ex}}\frac{6}{15}$ are unlike fractions with the same numerator.

The fractions can be ordered as, $\frac{6}{15}>\frac{6}{13}>\frac{6}{14}$ because the unlike fraction with the highest denominator will be the smallest among unlike fractions with the same numerator.
Comparison of unlike fractions with different numerator:
In order to compare unlike fractions, we have to convert all the  different denominators into the same denominators such as like fractions

Let's take the fractions $\frac{4}{5},\frac{2}{3},\frac{6}{7},\frac{24}{10},\frac{45}{15}$.

Do follow the steps below to compare unlike fractions.
i) Take LCM (Least Common Multiple) of all the denominators.

ii) Make the denominators of all the fractions into LCM.

iii) Compare the numerators of the like fractions, the fraction with the greatest numerator will be the greatest fraction.
Example:
Find the greatest fraction among $\frac{4}{5},\frac{2}{3},\frac{6}{7},\frac{24}{10},\frac{45}{15}$

i) LCM of all the denominators $$5, 3, 7$$ is $$105$$.

ii)$\frac{4×21}{5×21},\frac{2×35}{3×35},\frac{6×15}{7×15}$ $$=$$ $\frac{84}{105},\frac{70}{105},\frac{90}{105}$
• To convert $$5$$ into $$105$$, $$105 ÷ 5 = 21$$, multiply $$4/5$$ with $$21$$ in both numerator and denominator to get $$105$$ as the denominator.
• To convert $$3$$ into $$105$$, $$105 ÷ 3 = 35$$, multiply $$2/3$$ with $$35$$ in both numerator and denominator to get $$105$$ as the denominator.
• To convert $$7$$ into $$105$$, $$105 ÷ 7 = 15$$, multiply $$6/7$$ with $$15$$ in both numerator and denominator to get $$105$$ as the denominator.
iii) Compare the numerators of like fractions, $$84$$, $$70$$ and $$90$$. Where $$90 > 84 > 70$$ so $\frac{90}{105}>\frac{84}{105}>\frac{70}{105}$.

The corresponding fractions are, $\frac{6}{7}>\frac{4}{5}>\frac{2}{3}$.

Hence, the greatest fraction among $\frac{4}{5},\frac{2}{3},\frac{6}{7},\frac{24}{10},\frac{45}{15}$ is $\frac{6}{7}$.