# The concept of mixed numbers - free lesson

Mixed numbers have a whole-number 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 1 3

“One and one-third”

 2 3 4

“Two and three-fourths”

1. Write what mixed numbers the pictures illustrate. Read the mixed numbers. Remember to use
“and” between the whole-number part and the fractional part.

 a. b. c. d. e. f.

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 whole-number part and a fractional part, such as 1 3 4 or  2 3 4 .

3. Mark the mixed numbers on the number lines.

 a.  1 2 6 ,   2 1 6 ,   2 5 6

 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.

 a. = 2

 b. =

 c. =

 d. =

 e. =

 f. =

This is a 1-liter 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.

 a.

 b.

 c.

8. Remember measuring lines in inches? Measure the lines using the ruler. Your answers will
be mixed numbers.

 a. ________ inches

 b. ________ inches

 c. ________ inches

9. Draw a line that is...

a.  4 3/4 inches long

b.
6 1/4 inches long

This lesson is taken from my book Math Mammoth Introduction to Fractions.

#### Math Mammoth Introduction to Fractions

A self-teaching worktext for 2nd-4th 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.