The concept of mixed numbers  free lesson
Mixed numbers have a wholenumber part and a fractional part. This fourth grade lesson shows the concept of a mixed number with the help of visual models and number lines.
Mixed numbers have two parts:
 the whole number part, and
 the fractional part.



1. Write what mixed numbers the pictures illustrate.
Read the mixed numbers. Remember to use
“and” between the wholenumber part and the fractional
part.
2. Draw
pie pictures to illustrate these mixed numbers.
a. 1 
1
2 

b. 2 
2
3 

c. 2 
3
5 

d. 4 
5
6 

e. 3 
5
8 

Study this number line carefully.
After 1, we have two ways of marking the fractions
for the tick
marks on the number line:
 either as fractions, such as 
7
4 
or 
11
4 
, counting all the fourth parts
from zero. 
 or as mixed numbers: with a
wholenumber part and a fractional part, such as 1 
3
4 
or 2 
3
4 
. 

3. Mark the mixed
numbers on the number lines.

b. 1 
5
8 
, 1 
1
8 
, 2 
4
8 
, 2 
6
8 

c. 1 
1
5 
, 3 
4
5 
, 2 
2
5 
, 4 
3
5 

4. Use the number lines above, and write these
fractions as mixed numbers.
a. 
8
6 
= 


b. 
13
6 
= 


c. 
17
6 
= 


d. 
11
8 
= 


e. 
21
8 
= 


f. 
13
5 
= 


g. 
9
5 
= 


h. 
21
5 
= 


You can use pie pictures
to write
a mixed number
as a fraction.
Just count the fractional
parts. 

Count all the thirds. You
should get four thirds.
So, 1 
1
3 
=

4
3 
. 



Count all the fourths. You
should get eleven fourths.
So, 2 
3
4 
=

11
4 
. 


5.
Match. 
1 
3
4 


9
4 

2 
1
4 


9
8 

1 
1
8 


12
5 


3 
1
5 


11
8 


1 
3
8 


7
4 


2 
2
5 


16
5 

6. Write these both as mixed numbers AND
as fractions.
This
is a 1liter pitcher. In other words, when it is full,
it holds 1 liter of water. It is divided into fourths. 
Here we have 1 
1
4 
liters
of water. 

7. Write a mixed number to tell how much water is in
the pitchers.
8. Remember measuring lines in inches?
Measure the lines using the ruler. Your answers will
be mixed numbers.
9. Draw a line that is...
a. 4 3/4
inches long
b. 6 1/4 inches long
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.
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