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.
Adding the fractions:

\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

Read Solution

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

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

Read 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

Read Solution

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

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

Read Solution

(05) Add the below fractions;
\mathtt{\ \frac{3}{13} \ ,\ \frac{11}{13} \ \ \&\ \ \frac{12}{13}}

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

Read Solution