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Adding Fractions with Like Denominators

Fractions are mainly used for the separation of the two quantities. For the separation of two quantities, fraction uses a horizontal line. Two types of part are present in the fractions. They are called as the numerator and the denominator. When doing addition, if the denominators are same for both of the fractions terms means then it is called as the like denominators. Adding fractions with like denominators or adding like fractions which gives the sum of two or more fractions.

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How to Add Fractions with Like Denominators

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Below are the steps of how to add fractions with common denominators-

Step 1: Check all fractions have the same denominators or not. If denominators are same move to step 2.

Step 2: Add the numerators together.

Step 3: The total sum of numerators is the numerator of resulting fraction.

Step 4: Denominators remains same in the answer as the fractions have like denominators.

Step 5: Simplify the result (if needed)

Below you can see the solved examples-

Solved Examples

Question 1: Add the fractions $\frac{42}{5}$ and $\frac{14}{5}$
Solution:
Step 1: Given fractions: $\frac{42}{5}$ and $\frac{14}{5}$ are like fractions[Since denominators are same]

Step 2: Add the numerators together

$\frac{42}{5}$ + $\frac{14}{5}$ = $\frac{(42 + 14)}{5}$ = $\frac{56}{5}$

Step 2: Keep the denominator same

= $\frac{56}{5}$

Step 3: Simplify

$\frac{56}{5}$ = 11.2 (or) we can express this as a mixed number

$\frac{56}{5}$ = 11$\frac{1}{5}$

Hence $\frac{42}{5}$ + $\frac{14}{5}$


Correct answer is 11.2 (or) 11$\frac{1}{5}$
Question 2: Add the fractions $\frac{13}{2}$ and $\frac{109}{2}$
Solution:
Step 1: The denominators should be same.

Step 2: We subtract the numerators, when the denominators are same.

Step 3: Now simplify the fractions.

Step 1: Given fractions: $\frac{13}{2}$ and $\frac{109}{2}$ are like fractions [Since denominators are same]

Step 2: Add the numerators together

$\frac{13}{2}$ + $\frac{109}{2}$ = $\frac{(13 + 109)}{2}$ = $\frac{122}{2}$

Step 2: Keep the denominator same

= $\frac{122}{2}$

Step 3: Simplify

$\frac{122}{2}$ = 61


Correct answer is 61
Question 3: Add $\frac{125}{12}$ and $\frac{31}{12}$
Solution:
Step 1:  $\frac{125}{12}$ and $\frac{31}{12}$ 

Step 2: Add the numerators together

$\frac{125}{12}$ + $\frac{31}{12}$ = $\frac{(125 + 31)}{12}$ = $\frac{156}{12}$

Step 2: Keep the denominator same

= $\frac{156}{12}$

Step 3: Simplify

$\frac{156}{12}$ = 13


Correct answer is 13
Question 4: Solve $\frac{9}{42}$ + $\frac{102}{42}$ + $\frac{54}{42}$
Solution:

Denominators are same of given fractions.


Step 1:
 Add the numerators together


$\frac{9}{42}$ + $\frac{102}{42}$ + $\frac{54}{42}$
 = $\frac{(9 + 102 + 54)}{42}$ = $\frac{165}{42}$


Step 2:
 Keep the denominator same


$\frac{165}{42}$


Step 3: 
Simplify


$\frac{165}{42}$
 = $\frac{55}{14}$ = 3.928 (or) 3 $\frac{39}{42}$



Correct answer is 3.928 (or) 3 $\frac{39}{42}$
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