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 Sub Topics Fractions are the numbers which we can write in form of one number divided by another number. Here we express it as $\frac{p}{q}$, so we write āpā as the numerator and āqā as the denominator. We know that all the mathematical operators can be performed on the fractions. Here we will work on adding fractions. To learn how to add fractions, see whether the two given fractions share a common denominator or not. If not make the denominators same by using mathematical operations, find their sum by adding the numerators. Addition of the fractions with different denominators is possible, if we make the denominators same. If there are mixed fractions, convert the mixed fractions to improper fractions. Also if we add 0 to any fraction, the result remains the same.

Steps for adding fractions are explained below.
1. For the given problem if the fractions have a different denominator find the common denominator and go to next step, else add the fractions.
2. Make equivalent fractions with the new denominator.
4. Simplify the fraction.
Below you can see few examples
Example 1: Add $\frac{3}{5}$ + 0

Solution: $\frac{3}{5}$ + 0

= $\frac{3}{5}$

Example 2: Add $\frac{12}{7}$ +$\frac{10}{7}$

Solution:
$\frac{12}{7}$ + $\frac{10}{7}$

= $\frac{12+10}{7}$

= $\frac{22}{7}$

## Adding Fractions with Whole Numbers

Few examples for adding fractions with whole numbers are explained below.

Example 1: Add the fraction value $\frac{2}{5}$ with the whole number 6.

Solution: Steps to be followed to add the fraction value $\frac{2}{5}$ with the whole number 6.
Add: $\frac{2}{5}$ + 6

With the whole number 6 multiply and divide by 5 to get the fraction value.

= $\frac{2}{5}$ + 6 * $\frac{5}{5}$

= $\frac{2}{5}$ + $\frac{30}{5}$

= $\frac{32}{5}$

Therefore, the solution is $\frac{32}{5}$.

Example 2: Add the fraction value $\frac{7}{8}$ with the whole number 3.

Solution: Steps to be followed to add the fraction value $\frac{7}{8}$ with the whole number 3.
Add: $\frac{7}{8}$ + 3

With the whole number 3 multiply and divide by 8 to get the fraction value.

= $\frac{7}{8}$ + 3 * $\frac{8}{8}$

= $\frac{7}{8}$ + $\frac{24}{8}$

= $\frac{31}{8}$

Therefore, the solution is $\frac{31}{8}$

## Adding Fractions with Like Denominators

Steps to followed for like denominators.
1. Add the numerators of all the fractions together.
2. Total of the numerators is the numerator of the answer.
3. Denominators will remain same for the answer denominator.
4. Simplify the fraction to its lowest terms.
Example 1: Add $\frac{5}{6}$ and $\frac{4}{6}$

Solution: For the given problem the denominators are same so we need to add only the numerators.

$\frac{5}{6}$ + $\frac{4}{6}$ = $\frac{5+4}{6}$

= $\frac{9}{6}$

Simplifying the above fraction we get, $\frac{3}{2}$

Therefore, the answer is $\frac{3}{2}$

## Adding Fractions with Unlike Denominators

Steps for adding unlike denominators are explained below.
1. Find the least common denominator of the fractions. Find a common denominator.
2. Build each fraction so that both the denominators are equal.
3. Add the numerators of the fraction.
4. Simplify the fraction if possible.
Example 1: Add $\frac{3}{5}$ and $\frac{1}{3}$
Solution:
The given two fractions $\frac{3}{5}$ and $\frac{1}{3}$ are unlike fractions.

LCD of 5 and 3 = 15
Step 2: So, $\frac{3*3}{5*3}$ + $\frac{1*5}{3*5}$

= $\frac{9}{15}$ + $\frac{5}{15}$

Step 3: From above we see that the denominators are same so we can add the fractions.

= $\frac{9+5}{15}$

= $\frac{14}{15}$

Therefore, the solution is $\frac{14}{15}$

Given below are few examples explaining adding fractions with variables.

Example 1: Add $\frac{7x}{5}$ and $\frac{4x}{5}$

Solution: For the given problem we have the same denominators so we can add the numerators.

$\frac{7x}{5}$ + $\frac{4x}{5}$

= $\frac{7x + 4x}{5}$

= $\frac{11x}{5}$

Therefore the solution is $\frac{11x}{5}$

Example 2: Add $\frac{2x}{4}$ + $\frac{x}{5}$

Solution: The least common denominator of 4 and 5 is 20
So, $\frac{2x*5}{4*5}$ + $\frac{x*4}{5*4}$

= $\frac{10x}{20}$ + $\frac{4x}{20}$

Step 3: From above we see that the denominators are same so we can add the fractions.

= $\frac{10x+4x}{20}$

= $\frac{14x}{20}$

After simplifying we get, $\frac{7x}{10}$