# How to add fractions with same denominator?

In this post we will learn addition of fraction with same denominator.

The concept is simple and requires basic understanding of addition principle.

## Adding Fractions with same denominator

Fractions with same denominator is added by simply adding the numerators of all fractions and retaining the given denominator.

In the above image A/C and B/C are the fractions with same denominator C.

The addition is done by adding the numerators (A + B) and keeping the same denominator (C) in the final result.

### Understanding Fraction Addition using graphical representation

Here we will understand the concept of fraction addition using circular chart.

Let us take two fractions 2/4 and 1/4 for addition.

Fraction 2/4 mean that the object is divided into 4 equal parts out of which 2 parts are shaded.

Similarly fraction 1/4 mean that the object is divided into 4 equal parts out of which 1 part is shaded.

The above image explains the addition of fractions.

\mathtt{\Longrightarrow \ \frac{2}{4} \ +\ \frac{1}{4} \ }\\\ \\ \mathtt{\Longrightarrow \ \frac{2\ +\ 1}{4}}\\\ \\ \mathtt{\Longrightarrow \ \frac{3}{4}}

Here the fraction 3/4 mean that the object is divided into 4 parts out of which 3 part is shaded.

Note:
The addition of fraction with same denominator is a straightforward process. But if the fractions have different denominator, the process get tedious and complex.
We will learn fraction addition with different denominator in our next post.

### Examples of Fraction addition with same denominator

Now we will look at some of the examples on fraction additions.
The examples will help to gain in-depth understanding of the concept.

Example 01
Add the fractions \mathtt{\frac{3}{7} \ \&\ \frac{4}{7}}

Solution
Both the fractions have same denominator.
Simply add the numerator & retain the denominator.

\mathtt{\Longrightarrow \ \frac{3}{7} \ +\ \frac{4}{7} \ }\\\ \\ \mathtt{\Longrightarrow \ \frac{3\ +\ 4}{7}}\\\ \\ \mathtt{\Longrightarrow \ \frac{7}{7}}

Simplifying the fraction further.
Divide numerator and denominator by 7

\mathtt{\Longrightarrow \ \frac{7\div 7}{7\div 7}}\\\ \\ \mathtt{\Longrightarrow \ 1}

Hence, 1 is the solution.

Example 02
Add the fractions \mathtt{\frac{8}{15} \ \&\ \frac{11}{15}}

Both the fractions have same denominator.

\mathtt{\Longrightarrow \ \frac{8}{15} \ +\ \frac{11}{15} \ }\\\ \\ \mathtt{\Longrightarrow \ \frac{8\ +\ 11}{15}}\\\ \\ \mathtt{\Longrightarrow \ \frac{19}{15}}

Hence, 19/15 is the solution of addition.

Example 03
Add the fractions \mathtt{\frac{1}{5} \ ,\frac{3}{5} \ \&\ \frac{4}{5}}

Adding the fractions with same denominator;

\mathtt{\Longrightarrow \ \frac{1}{5} \ +\ \frac{3}{5} \ +\ \frac{4}{5} \ }\\\ \\ \mathtt{\Longrightarrow \ \frac{1\ +\ 3\ +\ 4}{5}}\\\ \\ \mathtt{\Longrightarrow \ \frac{8}{5}}

Hence, 8/5 is the solution of addition.

Example 04
\mathtt{Add\ \frac{17}{52} \ \ \&\ \frac{13}{52}}

Both the fractions have same denominator.
Adding the numerator and keeping the same denominator.

\mathtt{\Longrightarrow \ \frac{17}{52} \ +\ \frac{13}{52} \ \ }\\\ \\ \mathtt{\Longrightarrow \ \frac{17\ +\ 13}{52}}\\\ \\ \mathtt{\Longrightarrow \ \frac{30}{52}}

Simplifying the fraction by dividing numerator and denominator by 2.

\mathtt{\Longrightarrow \ \frac{30\div 2}{52\div 2}}\\\ \\ \mathtt{\Longrightarrow \ \frac{15}{26}}

The fraction cannot be simplified further.

Hence, 15/26 is the solution.

Example 05
Add the fraction \mathtt{\frac{5}{2} \ \ \&\ \ 1}

Given are the fraction 5/2 and number 1.

1 can be converted into fraction as 2/2.

Now we have same denominator fraction 5/2 & 2/2.

Adding the fraction as described above:

\mathtt{\Longrightarrow \ \frac{5}{2} \ +\ \frac{2}{2} \ \ }\\\ \\ \mathtt{\Longrightarrow \ \frac{5\ +\ 2}{2}}\\\ \\ \mathtt{\Longrightarrow \ \frac{7}{2}}

Hence, fraction 7/2 is the solution.

## Questions on Addition of fraction with same denominator

(01) Add the fractions \mathtt{\frac{16}{5} \ \ \&\ \ \frac{18}{5}}

(a) 37/5
(b) 27/5
(c) 34/5

Option (c) is correct

Explanation:
Both the fractions have same denominator.
SO simply add the numerator and retain the same denominator.

\mathtt{\Longrightarrow \ \frac{16}{5} \ +\ \frac{18}{5} \ \ }\\\ \\ \mathtt{\Longrightarrow \ \frac{16\ +\ 18}{5}}\\\ \\ \mathtt{\Longrightarrow \ \frac{34}{5}}

Hence, 34/5 is the solution.

(02) Add the numbers \mathtt{\frac{13}{7} \ \ \&\ \ 1}

(a) 10/7
(b) 20/7
(c) 25/7

Option (b) is correct

Explanation:
The numbers given are 13/7 and 1

1 can be written as 7/7

Now the fractions are 13/7 and 7/7.

\mathtt{\Longrightarrow \ \frac{13}{7} \ +\ \frac{7}{7} \ \ }\\\ \\ \mathtt{\Longrightarrow \ \frac{13\ +\ 7}{7}}\\\ \\ \mathtt{\Longrightarrow \ \frac{20}{7}}

Hence, fraction 20/7 is the solution.

(03) Add the fractions \mathtt{\frac{\mathtt{25}}{3} ,\frac{19}{3} \ \ \&\ \ \frac{11}{3}}

(a) 55/3
(b) 55/2
(c) 66/2

Option (a) is correct

Explanation:
All the fractions have same denominator.

\mathtt{\Longrightarrow \ \frac{25}{3} \ +\ \frac{19}{3} \ +\ \frac{11}{3} \ \ }\\\ \\ \mathtt{\Longrightarrow \ \frac{25\ +\ 19+\ 11}{3}}\\\ \\ \mathtt{\Longrightarrow \ \frac{55}{3}}

Hence, fraction 55/3 is the solution.

(04) Add the fractions, \mathtt{\frac{1}{50} \ \&\ \frac{3}{50}}

(a) 3/50
(b) 2/25
(c) 2/50

Option (b) is correct

Explanation:
Adding the fractions with same denominator;

\mathtt{\Longrightarrow \ \frac{1}{50} \ +\ \frac{3}{50} \ \ \ }\\\ \\ \mathtt{\Longrightarrow \ \frac{1\ +\ 3}{50}}\\\ \\ \mathtt{\Longrightarrow \ \frac{4}{50}}

We can simplify the fraction further.
Divide numerator and denominator by 2.

\mathtt{\Longrightarrow \ \frac{4\div 2}{50\div 2}}\\\ \\ \Longrightarrow \frac{2}{25}

Hence, fraction 2/25 is the solution.

\mathtt{\ \frac{3}{13} \ ,\ \frac{11}{13} \ \ \&\ \ \frac{12}{13}}

(a) 45/13
(b) 25/13
(c) 2

Option (c) is correct

Explanation:
Adding the fractions with same denominator.

\mathtt{\Longrightarrow \ \frac{3}{13} \ +\ \frac{11}{13} +\frac{12}{13} \ \ \ }\\\ \\ \mathtt{\Longrightarrow \ \frac{3\ +\ 11\ +\ 12}{13}}\\\ \\ \mathtt{\Longrightarrow \ \frac{26}{13}}

We can further simplify the fraction.
Divide numerator and denominator by 13.

\mathtt{\Longrightarrow \ \frac{26\div 13}{13\div 13}}\\\ \\ \mathtt{\Longrightarrow \frac{2}{1}}

Hence, number 2 is the solution.