Jamit Fractions  Lesson Contents  
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Lesson 7: Adding and Subtracting Fractions

Find  1  +  2 
5  5 
Both fractions have the same denominator of 5, so we can simply add the numerators:
1  +  2  =  3 
5  5  5 
1  
5  
+  
2  
5  
=  
3  
5  
Find  7    3 
8  8 
Both fractions have the same denominator of 8, so we can simply subtract the numerators:
7    3  =  4  =  1 
8  8  8  2 
NOTE that the result was simplified (the numerator and the denominator divided by 4).
7  
8  
  
3  
8  
=  
4  
8  
=  
1  
2 
Find  11  +  3 
12  12 
Solution:
11  +  3  =  14  =  1  2  =  1  1 
12  12  12  12  6 
NOTE that the result was changed to a mixed fraction and then simplified.
To add or subtract fractions with
different denominators we must first
make the dominators the same
(by finding the Lowest Common Denominator
and using equivalent fractions).
NOTE: You have learned how to find the Lowest Common Denominator before (chapters 4 and 5).
Find  3    2 
4  3 
Solution:
Since the fractions have different denominators, they cannot be subtracted
until they have the same denominators.
We can express both fractions as twelfths.
3  =  9  and  2  =  8  
4  12  3  12 
9    8  =  1  
12  12  12 
Find  5  +  2 
6  3 
Solution:
Since the fractions have different denominators, they cannot be added until
they have the same denominators.
We can express both fractions as sixths.
2  =  4  
3  6 
5  +  3  =  8  =  1  2  =  1  1 
6  6  6  6  3 
NOTE that the result was changed to a mixed fraction and simplified.
To add mixed fractions
add the
whole parts
of the mixed fractions first
and then
the fraction parts..
Find  2  1  +  3  2 
7  7 
Solution:
2  1  +  3  2  =  (2 + 3)  + (  1  +  2  ) =  5 +  3  =  5  3 
7  7  7  7  7  7 
Find  3  8  +  5  5 
9  6 
Solution:
3  8  +  5  5  =  (3 + 5)  + (  8  +  5  ) =  Must first make the denominators equal 
9  6  9  6 
8  + (  16  +  15  ) =  8  31  =  (8 + 1)  13  =  9  13 
18  18  18  18  18 
NOTE that the resulting fraction part was improper , therefore it was changed to a mixed fraction.
To subtract mixed fractions subtract the whole parts of the mixed fractions
first and then the fraction parts.
But what to do if the left side fraction part is smaller than the right side
fraction part?
Find  7  2    2  4 
5  5 
Solution:
7  2    2  4  =  (7  2)  + (  2    4  ) =  5  + (  2    4  ) =  Our problem is  2  <  4 
5  5  5  5  5  5  5  5 
4  + (  5  +  2    4  ) =  Take 1 from 5 and add it to  2 
5  5  5  5 
(Remember? 1 =  5  )  
5 
4  +(  7    4  ) =  4  3  
5  5  5 
Find  1    2 
3 
Solution: 1 =  3  , therefore 
3 
1    2  =  3    2  =  1 
3  3  3  3 
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