There are two different methods of subtracting mixed fractions. They are,

- Subtracting mixed fractions with a common denominator
- Subtracting mixed fractions with a different denominator

### Subtracting Mixed Fractions with a Common Denominator

The difference of mixed fractions with common or same denominator can be obtained through the following steps

**Step 1:** Express the mixed fraction as improper fractions.

**Step 2:** Find the difference of the numerators.

**Step 4:** Retain the common denominator.

**Step 5: **Difference of the mixed fractions $\frac{Difference\ of\ numerators\ from\ step3}{Common\ Denominator}$### Examples on Subtracting Mixed Fractions with a Common Denominator

Subtract the mixed fractions 5

$\frac{2}{3}$ - 3

$\frac{1}{3}$We write the mixed fractions as improper fractions

5

$\frac{2}{3}$ =

$\frac{(5 \times 3)+2}{3}$ $\frac{17}{3}$ 3

$\frac{1}{3}$ =

$\frac{(3 \times 3)+1}{3}$ $\frac{10}{3}$5

$\frac{2}{3}$ - 3

$\frac{1}{3}$ =

$\frac{17}{3}$ -

$\frac{10}{3}$ Here the both fractions have a common denominator, so we can subtract the numerators.

5$\frac{2}{3}$ - 3$\frac{1}{3}$ = $\frac{17}{3}$ - $\frac{10}{3}$

$\frac{17-10}{3}$

=$\frac{7}{3}$

=2$\frac{1}{3}$

### Subtracting mixed fractions with different denominators

Convert the mixed fraction into a improper fraction to begin the operation of subtraction.

Multiply the whole number with the denominator and add the numerator to convert this into a new improper fraction.

**Step 1**: Find the LCD of the fractions

**Step 2**: After finding the LCD, we need to change the fractions into equivalent fractions having a common denominator

**Step 3**: Divide the denominator of each fraction into a LCD and then multiply the result with the fraction’s numerator and place it over the LCD.

**Step 4**: Subtract the numerator and get the final answer**Example of subtracting mixed fractions with different denominators**:

Subtract 1 $\frac{1}{4}$ – 1$\frac{1}{3}$ – 1$\frac{1}{6}$

Convert into $\frac{5}{4}$ – $\frac{4}{3}$ – $\frac{7}{6}$

**Step 1:** Find the LCD of the fractions

**Step 2:** LCD is found to be 12

**Step 3: **Divide the denominator of each fraction into LCD and then multiply the result with the fraction’s numerator and place it over the LCD $\frac{(15 – 16 – 14)}{12}$

**Step 3:** Subtract the numerators (-15)

Reduce the answer if required $\frac{-15}{12}$ = $\frac{-5}{4}$ = - 1 $\frac{1}{4}$