### Theory:

Subtraction of fractions:

**like, unlike and mixed**), different methods should be used to solve which are discussed with examples as follows.

**1. 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:

$\frac{2}{3}-\frac{8}{3}=\frac{-6}{3}=-2$

**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:

**Consider an expression**$\frac{9}{6}-\frac{14}{2}$

Apply the above theory to simplify the expression.

**Step 1)**LCM of \(2\) and \(6\) is \(6\).

**Step 2)**Change both denominators as \(6\).

To change \(6\) as \(6\), multiply numerator and denominator with \(1\), $\frac{9\times 1}{6\times 1}$

To change \(2\) as \(6\), multiply numerator and denominator with \(3\), $-\frac{14\times 3}{2\times 3}$

**Step 3)**Subtract the numerator of the fractions $\phantom{\rule{0.147em}{0ex}}\frac{9}{6}-\frac{42}{6}=\frac{-33}{6}$

**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.