When the fractions have the same denominator, we add the
numerators and keep the same denominator
1 

2 

3 
^{____} 
+ 
^{____} 
^{=} 
^{____} 
4 

4 

4 
Example 2: Add fractions with unlike
(different) denominators.

4 

2 
Add the fractions 
^{____} 
+ 
^{____} 

7 

5 
Solution to example 2:
step 1: Find the lowest
common multiple (LCM) of the two denominators.
The LCM of 7 and 5 is 35.
step 2: Write equivalent
fractions with a lowest common denominator (LCD) equal to the LCM.
4 

4 x 5 

20 
^{____} 
= 
^{____} 
^{=} 
^{____} 
7 

7 x 5 

35 
and
2 

2 x 7 

14 
^{____} 
= 
^{____} 
^{=} 
^{____} 
5 

5 x 7 

35 
step 3: Replace the given
fractions by their equivalent and add the fractions with like denominator.
4 

2 

20 

14 

34 
^{____} 
+ 
^{____} 
^{=} 
^{____} 
^{+} 
^{____} 
^{=} 
^{____} 
7 

5 

35 

35 

35 
step 3: Reduce the fraction
if possible.
The fraction obtained above cannot be further reduced.
Example 3: Add fractions mixed numbers.


2 


5 
Add the mixed
numbers 
3 
^{____} 
+ 
2 
^{____} 


3 


7 
Solution to example 3:
step 1: Add the whole numbers
3 + 2 = 5
step 2: Find the LCD, equivalent fractions with common denominator and add the
fractions.
2 

5 

14 

15 

29 
^{____} 
+ 
^{____} 
^{=} 
^{____} 
^{+} 
^{____} 
^{=} 
^{____} 
3 

7 

21 

21 

21 
step 3: Reduce and write the
fraction as a mixed number if possible.
29 


8 
^{____} 
^{=} 
^{1} 
^{____} 
21 


21 
step 4: Add the
whole number obtained in step 1 and the mixed number obtained in step 3



8 


8 
5 
^{+} 
1 
^{____} 
= 
6 
^{____} 



21 


21 
Questions with answers: Add and reduce if possible the following
fractions and mixed numbers.
1.
1 

3 
^{______} 
+ 
^{______} 
5 

5 
2.
3 

4 
^{______} 
+ 
^{______} 
5 

7 
3.
4.

2 


9 
4 
^{______} 
+ 
2 
^{______} 

3 


11 