### Theory:

Addition of fractions:
When a fractional number is added with another fractional number, based on the type of the fractions (like, unlike or mixed) added, different methods can be followed.

1. Addition of Like fractions:
If all the fractions in the addition operation have the same denominator, then add the numerator and write the result as a fractional number with the same denominator.
Example:
$\frac{1}{2}+\frac{5}{2}+\frac{7}{2}=\frac{13}{2}$
2. Addition of Unlike fractions:
If 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) Add the numerator of the fractions.
Find the value $$(1/2)$$ $$+$$ $$(2/3)$$

Step 1: LCM of $$(2, 3)$$ $$=$$ $$6$$

Step 2: To change $$2$$ to $$6$$ multiply numerator and denominator by $$3$$, $\frac{1×3}{2×3}=\frac{3}{6}$
Step 3: And the numerator of all the fraction, $\frac{3}{6}+\frac{4}{6}=\frac{7}{6}$
3. Addition of mixed fractions:
Mixed fractions can be written as a whole part plus a fraction. Add the whole parts separately and add the fractions.
Example:
Add$\phantom{\rule{0.147em}{0ex}}3\frac{6}{2}+2\frac{3}{2}$

Step 1: Add the whole parts separately.

Step 2: Add the proper fractions separately.

$$3+2$$ $$=$$ $$5$$; $\frac{6}{2}+\frac{3}{2}=\frac{9}{2}$

$=5+\frac{9}{2}=\frac{19}{2}$