### Theory:

Subtraction of fractions:

When a fractional number is subtracted with another fractional number, based on the type of the fractions (like, unlike and mixed), different methods should be used to solve which are discussed with examples as follows.

Subtraction of Like fractions:
If all the fractions in the subtraction operation have the same denominator, then subtract the numerator and then write the answer as a fractional number with the same denominator.
Example:
$\frac{2}{3}-\frac{8}{3}=\frac{-6}{3}=-2$
Subtraction of Unlike fractions:
If all the fractions have different denominators, change the fractions to like fractions. To change unlike fractions to like fractions follow the below steps:

Step i) Take LCM of both the denominators.
Step ii) Make the denominator of all the fractions to LCM.
Step iii) Subtract the numerators of all the fractions.
Example:
$\begin{array}{l}\frac{9}{6}-\frac{14}{2}\\ \\ \mathit{Step}\phantom{\rule{0.147em}{0ex}}i\right)\phantom{\rule{0.147em}{0ex}}\mathit{LCM}\phantom{\rule{0.147em}{0ex}}\mathit{of}\phantom{\rule{0.147em}{0ex}}2\phantom{\rule{0.147em}{0ex}}\mathit{and}\phantom{\rule{0.147em}{0ex}}6\phantom{\rule{0.147em}{0ex}}\mathit{is}\phantom{\rule{0.147em}{0ex}}6.\\ \\ \mathit{Step}\phantom{\rule{0.147em}{0ex}}\mathit{ii}\right)\phantom{\rule{0.147em}{0ex}}\mathit{Change}\phantom{\rule{0.147em}{0ex}}\mathit{both}\phantom{\rule{0.147em}{0ex}}\mathit{denominators}\phantom{\rule{0.147em}{0ex}}\mathit{as}\phantom{\rule{0.147em}{0ex}}6,\\ \\ \mathit{To}\phantom{\rule{0.147em}{0ex}}\mathit{change}\phantom{\rule{0.147em}{0ex}}6\phantom{\rule{0.147em}{0ex}}\mathit{as}\phantom{\rule{0.147em}{0ex}}6,\mathit{multiply}\phantom{\rule{0.147em}{0ex}}\mathit{numerator}\phantom{\rule{0.147em}{0ex}}\mathit{and}\phantom{\rule{0.147em}{0ex}}\mathit{denominator}\phantom{\rule{0.147em}{0ex}}\mathit{by}\phantom{\rule{0.147em}{0ex}}1,\frac{9×1}{6×1}\\ \\ \mathit{To}\phantom{\rule{0.147em}{0ex}}\mathit{change}\phantom{\rule{0.147em}{0ex}}2\phantom{\rule{0.147em}{0ex}}\mathit{as}\phantom{\rule{0.147em}{0ex}}6,\mathit{multiply}\phantom{\rule{0.147em}{0ex}}\mathit{numerator}\phantom{\rule{0.147em}{0ex}}\mathit{and}\phantom{\rule{0.147em}{0ex}}\mathit{denominator}\phantom{\rule{0.147em}{0ex}}\mathit{by}\phantom{\rule{0.147em}{0ex}}3,-\frac{14×3}{2×3}\\ \\ \mathit{Step}\phantom{\rule{0.147em}{0ex}}3:\mathit{Subtract}\phantom{\rule{0.147em}{0ex}}\mathit{the}\phantom{\rule{0.147em}{0ex}}\mathit{numerator}\phantom{\rule{0.147em}{0ex}}\mathit{of}\phantom{\rule{0.441em}{0ex}}\mathit{the}\phantom{\rule{0.147em}{0ex}}\mathit{fractions},\phantom{\rule{0.147em}{0ex}}\frac{9}{6}-\frac{42}{6}=\frac{-33}{6}\end{array}$
Subtraction of mixed fractions:
Mixed fractions can be written as a whole part plus a fraction, To subtract mixed fractions, first subtract whole parts separately and then subtract the fractions.