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.


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. 



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.
2. Shade parts. Then write an addition sentence. Look at the example.
a. Shade 
1
6

, then

3
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.
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. 



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.
A selfteaching worktext for 2nd4th grade that covers fractions and mixed numbers, adding and subtracting like fractions,
adding and subtracting mixed numbers, equivalent fractions, comparing fractions, and finding a fractional part using division.
Download ($5.30). Also available as a printed copy.
=> Learn more and see the free samples!
See more topical Math Mammoth books