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Adding Mixed Numbers

This free lesson teaches how to add mixed numbers with like fractional parts. We start with visual models (pies), and go on to add without them (abstract problems). The lesson is meant for fifth grade.

In the video below (also available at my Youtube channel) we study adding mixed numbers when their fractional parts are like fractions. This is not a difficult concept - all you need to remember is that if the sum of the fractional parts is more than 1, you need to convert that to "whole pies" and to a "leftover" fraction.




Adding mixed numbers

You can simply add the whole numbers
and fractional parts separately:

1

1

7

  +   5

3

7

  =   6

4

7

          or in columns →
   

1

1

7

+  5

3

7

6

4

7

However, many times the sum of the fractional parts goes over one whole pie.

+ =
1

3

6

+
1

4

6

=
2

7

6

  →    3

1

6

So first, simply add the fractional parts as usual. Then, change the fraction that is more
than one pie into one or more whole pies and a fractional part that is less than one pie.

1. These mixed numbers have a fractional part that is more than one “pie.” Change them so that
    the fractional part is less than one. The first one is done for you.

    a.  3

3

2

 →  4

1

2

b.  1

11

9

c.  6

7

4

d.  3

13

8

2. Write the addition sentences that the pictures illustrate and then add.

+ +

a.
 

+  

b.
 

 +

c.
 

 +  +

d.
 

e.   +     + 


3. Add.

    a.   3

2

3

 +   8

1

3

=
b.   4

4

5

 +   1

3

5

   
    c.   6

8

9

 +   1

2

9

d.   3

6

7

 +   2

4

7

4. Add.

a.

4

3

7

     
+

5

5

7

     
       
 

9

8

7

  →   10

1

7

b.

3

3

5

 
+

3

4

5

 
   
 

 

 

  → 
c.

4

6

9

 
+

2

7

9

 
   
d.

7

6

8

 
+

2

7

8

 
   

5. Tom has one string that is 7 3/8 inches long and another that is 5 7/8
    inches long. He tied them together. In making the knot, he lost 1 4/8
    inches from the total length. How long is the combined string now?


 

6. Gisele found two recipes for corn bread.
    If she uses recipe 1, she needs to double it.

    Which would use more flour, recipe 1
    doubled, or recipe 2?

Recipe 1:

1/2 cup cornmeal
3/8 cup wheat flour

(plus other ingredients)

 

Recipe 2:

1 cup cornmeal
1 cup wheat flour

(plus other ingredients)

   
    How much more?


 

7. Find the missing addend. Imagine drawing more in the picture.

a.   1

1

2

+              = 3
b.   2

2

3

+              = 5
c.   1

1

4

+              = 5
d.   2

3

4

+              = 8


Sometimes the sum of the fractional
parts can be two or more whole pies.
Just figure out how many whole pies
you can make from the fractional parts
and add them to the whole number part.

    + +  

=

 

1

5

6

 +  1

3

6

 +  1

5

6

 =   3

13

6

  →    5

1

6

8. Convert these mixed numbers so that the fractional part is less than one.

    a.  3

13

5

b.  1

11

4

c.  6

13

4

d.  3

19

8

9. Add these mixed numbers.

    a.   3

1

6

 +   2

5

6

 =
b.   4

4

5

 +  1

2

5

  +  5

2

5

 = 
   
    c.   6

4

8

 +  1

6

8

 +  1

7

8

 = 
d.   3

6

10

 +  3

8

10

 +  

9

10

 = 

10. Add the mixed numbers.

a.

10

7

9

 
 

2

5

9

 
+

3

8

9

 
   
       → 
b.

1

5

11

 
 

3

9

11

 
+

2

8

11

 
   
       → 
c.

2

5

6

 
 

5

4

6

 
+

2

3

6

 
   
       → 
d.

1

7

10

 
 

 

9

10

 
+

10

6

10

 
   
       → 

11. Jeremy runs 2 ¼ miles four days a week.
      Robert runs 3 ½ miles three times a week. 
      Which boy runs more in one week?
      How much more?

 

12. Find the missing addends.

a.   2

1

4

 + 1

1

4

+            =  5
b.   3

2

5

 + 2

2

5

+            =  8
c.   2

1

3

 + 

2

3

 +            =  4

1

3




This lesson is taken from my book Math Mammoth Fractions 1.

Math Mammoth Fractions 1

A self-teaching worktext for 5th grade that teaches fractions and their operations with visual models. The book covers fractions, mixed numbers, adding and subtracting like fractions, adding and subtracting mixed numbers, adding and subtracting unlike fractions, and comparing fractions.

Download ($3.50). Also available as a printed copy.

Learn more and see the free samples!

See more topical Math Mammoth books



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