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Adding Like Fractions and Mixed Numbers

This free lesson teaches how to add like fractions and mixed numbers with like fractional parts using visual models (pies, fraction bars). It includes lots of exercises and is meant for fourth grade.

In the video below (also available at my Youtube channel), I explain how to add and subtract like fractions, first using visual models, and then advancing into abstract problems.




+ =

1

4

+

2

4

=   

3

4

It is easy to add fractions that have the same kinds of parts.

To add 

1

4

 and 

2

4

, think of the pie pieces. One fourth means

one piece, and two fourths means two pieces. In total we have
three pieces, and they are fourths. So, the answer is 3/4.

 

7

8

 + 

6

8

 =   

13

8

  =  1

5

8

In this picture we have shaded (added) seven slices and then another six slices. All the slices are eighth parts so we can just count how many eighths we get: 13 eighths.

But that makes more than one whole pie, so the answer is given as a mixed number.

1. Write an addition sentence.

a.   +    
 

2

5

+

2

5

=  
b.   +
c.   +

2. Shade parts. Then write an addition sentence. Look at the example.

a. Shade

1

6

, then

3

6

.

    

 

1

6

  +   

3

6

  =   

4

6

b. Shade

2

8

, then

5

8

.

   

 

c. Shade

3

12

, then 

5

12

, then 

2

12

.

  

 

 

d. Shade

1

10

, then 

3

10

, then 

4

10

.

  

e. Shade

3

8

, then 

7

8

.

     

 

 

f. Shade

3

4

, then 

3

4

.

  



3. Shade parts. Then write an addition sentence.

a. Shade

6

5

, then

1

5

.

   

         


 

b. Shade 2

1

2

, then 

1

2

.

  

c. Shade 1

2

10

, then  

6

10

.

    

 

d. Shade  

11

7

, then  

6

7

.

      

 

 

4. Add the fractions and mixed numbers. You can shade parts in the pictures, if you need help.

   

a.  1

2

10

 + 

2

10

 + 

7

10

 =

   

b. 

11

9

 + 

8

9

 =

   

c.  1

3

8

 + 

7

8

 =

 

This is a fraction strip. The whole numbers from 0 to 5 are written under the bolded black lines.

The shaded parts illustrate the addition   

4

5

 + 

4

5

  =  

8

5

  =  1

3

5

.

5. Add. Shade parts with different colors. Give your answer as a mixed number.

a. 

3

5

 + 

4

5

 =
b.  1

2

5

 + 

4

5

 =
   
c. 

13

10

 + 

6

10

 =
d.  1

3

8

 + 

6

8

 =


 We can “break apart” 7/8 in many different ways. From each “breakage” we can write an addition.

For example:    = and and
  

7

8

4

8

 + 

1

8

 +

2

8

Another way:   = and and
 

7

8

3

8

 + 

2

8

 +

2

8

6. Write each fraction as an addition in different ways. Think of breaking the fraction apart.

a. 

 

   

4

5

 =   +  
           
 

4

5

 =      
           
 

4

5

 =      
b. 

 

   

5

8

 =
     
 

5

8

 =
     
 

5

8

 =
c.

 

     =
     
   =
     
   =
d.

 

   

4

3

 =
     
   =
     
   =
e.   

 

 =
   
 =
      =
     
   =


How to add mixed numbers?   For example, what is  4

5

6

 + 3 

4

6

= ? 
Add the whole numbers first: 4 + 3 = 7. Then add the fractions:  

5

6

 + 

4

6

 = 

9

6

. That is more than

1 whole! So think of the 9/6 as 1 and 3/6, and add 1 to the whole number count. In total we get 8

3

6

.

7. Add the mixed numbers. Shade parts to help.

  

a.  1

3

5

  +  2

2

5

 =

b.  1

3

4

  +  1

2

4

 =

 

c.  1

3

8

  +  1

6

8

 =

d.  

8

9

  +  1

5

9

 =

e.  1

3

7

  +  2

6

7

 =

f.  

9

12

  +  1

7

12

 =

8. Write each mixed number as an addition in different ways.

a.  

 

     =
     
   =
     
   =
     
   =
b.

 

     =
     
   =
     
   =
     
   =



You will find free, printable worksheets for adding like fractions here.


This lesson is taken from Maria Miller's book Math Mammoth Introduction to Fractions, and posted at www.HomeschoolMath.net with permission from the author. Copyright © Maria Miller.





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