### Theory:

Addition of 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 \(3\), $\frac{1\times 3}{2\times 3}=\frac{3}{6}$

**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.

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

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