Mixed numbers and fractions:
how to convert from one to the other
This is a fifth grade lesson about fractions and mixed numbers. First, this lesson has some review exercises about mixed numbers. Then, we learn how to change mixed numbers into fractions  both the concept and the shortcut. Lastly, we convert improper fractions into mixed numbers by thinking of them as DIVISIONS.
Mixed numbers as pictures
1. Write the mixed numbers that these pictures illustrate.
a.  b. 
c. 

2. Draw pictures of “pies” that illustrate these mixed numbers.







3. Write the mixed number that is illustrated by each number line.


4. Write the fractions and mixed numbers that the arrows indicate.

5. Mark the fractions on the number lines.
a. 
10
6 
, 
17
6 
, 
12
6 
, 
5
6 
, 
14
6 
b. 
9
8 
, 
22
8 
, 
13
8 
, 
24
8 
, 
11
8 
6. a. Mark 1 
3
5 
on the number line. b. Write the mixed number that is 
4
5 
to its right: _______ 
c. Mark 2 
1
5 
on the number line. d. Write the mixed number that is 
3
5 
to its left: _______ 

7. Write as mixed numbers and as fractions.







8. May changed 5 
9 13 
into a fraction, and explained how the shortcut works. Fill in. 
There are ____ whole pies, and each pie has _____ slices. So ____ × ____
tells us the number of slices in the whole pies. Then the fractional part 9/13 means that  
we add _____ slices to that. In total we get ____ slices, each one a 13th part. So the fraction is 
. 
9. Write as fractions. Think of the shortcut.









Changing fractions to mixed numbers
That is solved by the division 58 ÷ 7! That division tells you how many 7s there are in 58. Now, 58 ÷ 7 = 8 R2. So you get 8 whole pies, with 2 slices or 2 sevenths left over.




The
Shortcut:
Think of the fraction bar as a division symbol, then DIVIDE.
The quotient tells 
10. Rewrite the “division problems
with remainders” as problems of “changing fractions to mixed
numbers.”
a. 47 ÷ 4 = 11 R3

b. 35 ÷ 8 = 4 R3

c. 19 ÷ 2 = ___ R ___


d. 35 ÷ 6 = ___ R ___

e. 72 ÷ 10 = ___ R ___

f. 22 ÷ 7 = ___ R ___

11. Write these fractions as mixed numbers (or as whole numbers, if you can).














This lesson is taken from Maria Miller's book Math Mammoth Fractions 1, and posted at www.HomeschoolMath.net with permission from the author. Copyright © Maria Miller.
Math Mammoth Fractions 1
A selfteaching 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.