Jamit Fractions - Lesson Contents 
 
For Parents or Teachers: Create printable worksheets for your kids based on this lesson. Please visit the Fraction Worksheets pages.

 

Lesson 7: Adding and Subtracting Fractions

 


  1. How to Add and Subtract Fractions.
  2. Adding and Subtracting Fractions with The Same Denominators.
  3. Adding and Subtracting Fractions with Different Denominators.
  4. Adding Mixed Fractions.
  5. Subtracting Mixed Fractions.
  6. Practice Game.



HOW TO ADD AND SUBTRACT FRACTIONS

To add fractions you have to:

  1. Make the  denominators the same using equivalent fractions.
  2. Add or subtract the numerators.
  3. Change the result to a mixed fraction if the numerator is larger than
    the denominator.
  4. Simplify the final result if possible.

ADDING OR SUBTRACTING FRACTIONS WITH THE SAME DENOMINATORS

Adding or subtracting fractions with the same denominator is easy. All you have to do is to add or subtract the numerators.
And it is always a good idea to make your result "nice" by converting it to a mixed number and simplifying if possible.

Example:

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

 

FilledRec.gif (981 bytes)emptyrec.gif (982 bytes)emptyrec.gif (982 bytes)emptyrec.gif (982 bytes)emptyrec.gif (982 bytes) 1
5
+  
FilledRec.gif (981 bytes)FilledRec.gif (981 bytes)emptyrec.gif (982 bytes)emptyrec.gif (982 bytes)emptyrec.gif (982 bytes) 2
5
             =                   
FilledRec.gif (981 bytes)FilledRec.gif (981 bytes)FilledRec.gif (981 bytes)emptyrec.gif (982 bytes)emptyrec.gif (982 bytes) 3
5
   

 

Example:

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).

FilledRec.gif (981 bytes)FilledRec.gif (981 bytes)FilledRec.gif (981 bytes)FilledRec.gif (981 bytes)FilledRec.gif (981 bytes)FilledRec.gif (981 bytes)FilledRec.gif (981 bytes)emptyrec.gif (982 bytes) 7
8
-  
FilledRec.gif (981 bytes)FilledRec.gif (981 bytes)FilledRec.gif (981 bytes)emptyrec.gif (982 bytes)emptyrec.gif (982 bytes)emptyrec.gif (982 bytes)emptyrec.gif (982 bytes)emptyrec.gif (982 bytes) 3
8
                 =                   
FilledRec.gif (981 bytes)FilledRec.gif (981 bytes)FilledRec.gif (981 bytes)FilledRec.gif (981 bytes)emptyrec.gif (982 bytes)emptyrec.gif (982 bytes)emptyrec.gif (982 bytes)emptyrec.gif (982 bytes) 4
8
=  
FilledRec.gif (981 bytes)emptyrec.gif (982 bytes) 1
2

 

Example:

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.


ADDING AND SUBTRACTING FRACTIONS WITH DIFFERENT DENOMINATORS.

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).

Example:

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    

 

Example:

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.


ADDING MIXED FRACTIONS

To add mixed fractions add the whole parts of the mixed fractions first
and
then the fraction parts
..

Example:

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

Example:

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.


SUBTRACTING MIXED FRACTIONS

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?

Example:

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  

 

Example:

Find 1 - 2
3
Solution:            1 = 3 , therefore
3
1 - 2 = 3 - 2 = 1
3 3 3 3

 

 


Site Links Jamit Fractions | Fraction Worksheets | Fraction Games | Online Games

Copyright 2009 - Adam Malinowski. (Member of CAL, Statutory Licence Schemes)