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

**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.

Adding the fractions:

\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.**

**(05) Add the below fractions; **

\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**.