The process for addition of unlike fractions is as follows:

1. Find the least common denominator of all the fractions

2. Rewrite the fractions to have the denominators equal to the LCD obtained in step 1

3. Add the numerators of all the fractions keeping the denominator value equal to the LCD obtained in step 1

4. Express the fraction in lowest terms.

### Examples on Adding Unlike Fractions

Given below are some of the examples on adding unlike fractions.

**Example 1:**

Find the sum of $\frac{5}{3}$ and $\frac{7}{4}$

**Solution:**

The denominators of the given fractions are 3 and 4.

The least common denominator (LCD) of 3 and 4 is 12.

Now, rewrite the fractions to have the denominators equal to the LCD

$\frac{5}{3}$ = $\frac{(5\times4)}{(3\times4)}$ = $\frac{20}{12}$

$\frac{7}{4}$ = $\frac{(7\times3)}{(4\times3)}$ = $\frac{21}{12}$

$\frac{5}{3}$ + $\frac{7}{4}$ = $\frac{20}{12}$ + $\frac{21}{12}$

Now, add the numerators

$\frac{5}{3}$ + $\frac{7}{4}$ = $\frac{(20 + 21)}{12}$ = $\frac{41}{12}$

Since 41 and 12 are co primes, $\frac{41}{12}$ is the answer.

**Example 2:**

Find the sum of $\frac{6}{5}$ , $\frac{7}{4}$ and $\frac{2}{3}$

**Solution:**

The denominators of the given fractions are 5, 4 and 3.

The least common denominator (LCD) of 5, 4 and 3 is 60.

Now, rewrite the fractions to have the denominators equal to the LCD

$\frac{6}{5}$ = $\frac{(6\times12)}{(5\times12)}$ = $\frac{72}{60}$

$\frac{7}{4}$ = $\frac{(7\times15)}{(4\times15)}$ = $\frac{105}{60}$

$\frac{2}{3}$ = $\frac{(2\times20)}{(3\times20)}$ = $\frac{40}{60}$

$\frac{6}{5}$ + $\frac{7}{4}$ + $\frac{2}{3}$ = $\frac{72}{60}$ + $\frac{105}{60}$ + $\frac{40}{60}$

Now, add the numerators.

Express the fractions in the lowest terms by canceling the common factors in the numerator and the denominator.

$\frac{215}{60}$ = $\frac{(5\times43)}{(5\times12)}$ = $\frac{43}{12}$

Since 43 and 12 are co primes, $\frac{43}{12}$ is the answer.