In order to add fractions, you should have the same denominator.

Let’s try these in different cases:

## Adding the fractions Having the same Denominator:

• If the denominator of both the numbers is the same, we leave it as it is and add the numerators.

Let’s understand it with an example:

$\frac{7}{2}$ +$\frac{4}{2}$ = $\frac{11}{2}$

In the above Example, if we add $\frac{7}{2}$ and $\frac{4}{2}$, we leave the denominator 2 as it is and add the numerators 7 and 4, i.e 7 + 4 = 11. The result of the fraction is $\frac{11}{2}$.

## Add Fractions with Coprime Denominators

• What are Co-prime Factors?

Coprime denominators: The denominators which do not have common factors.

Let’s study how to add co-prime factors?

Steps:

• You need to multiply the denominator to find the denominator of the resulting fraction.
• Multiply the numerator of one of the fractions by the denominator of the other or vice versa to get the numerator.

## Examples of addition of Fractions:

Let’s understand it with an example:

$\frac{10}{3}$ +$\frac{2}{4}$ =$\frac{10 X 4}{3 x 4}$ +$\frac{2 X 3}{4 X 3}$ = $\frac{40}{12}$ +$\frac{6}{12}$ = $\frac{46}{12}$

The denominators are 3 and 4, which are different and have no common factors,

so to calculate the numerator, you need to multiply 10 X 4 = 40 and 2 x 3 = 6, and add the results, 40 + 6 = 46, which would be the numerator of the answer.

Hence, the final answer to the addition is $\frac{46}{12}$

## Add Fractions with a Denominator that is the Divisor of the Other:

Let’s understand it with an example:

$\frac{10}{20}$ +$\frac{3}{4}$ = $\frac{10}{20}$ +$\frac{3 X 5}{4 X 5}$ = $\frac{10}{20}$ +$\frac{15}{20}$ = $\frac{10 X 15}{20}$ = $\frac{150}{20}$ = $\frac{15}{2}$
• As the denominator of these fractions are different, but as 4 is a factor of 20, which

is a multiple of 5.

• Multiply both the numerator and the denominator of $\frac{3}{4}$ by 5.
• You will get $\frac{15}{20}$.
• Now find the sum of both fractions.
• It will give the answer as $\frac{150}{20}$ which can be simplified further

to $\frac{15}{2}$.

## Add Fractions with the Least Common Multiple:

Let’s understand it with an example:

$\frac{3}{12}$ + $\frac{10}{8}$

Steps:

• The denominators of the added fractions are 12 and 8.
• Both of these are different with common factors.
• To determine the least common multiple, we need to factor the numbers.

12 = 22 X 3

8 = 23

• Find the highest power of any common factors to find the LCM – 24 = 23 x 3
• So, 24 is the common denominator.

To calculate the numerator of the fractions for adding or subtracting , divide the calculated LCM into the denominator.

• Next, Multiply the result with the numerator, $\frac{24}{12}$ = 2 and $\frac{6}{2}$ = 3
• $\frac{24}{8}$ = 3 and $\frac{30}{3}$ = 10
• The new fractions will be $\frac{3}{12}$ X $\frac{2}{2}$ and $\frac{10}{8}$ X $\frac{3}{3}$.
• Resulting Fraction – $\frac{30}{24}$.
• The sum of the two fractions is $\frac{36}{24}$
The answer is $\frac{3}{2}$