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The ideas in this fraction lesson are taken from Math Mammoth Fractions 1 book. Only a few examples of each problem type are shown; you should make more problems of each kind for the student.

Mixed numbers & how to convert a mixed number into a fraction
Free lesson plan from HomeschoolMath.net

This lesson has some review. Please don't go on with the lessons about adding and subtracting mixed numbers until you understand the topics in this lesson well.

Mixed numbers as pictures

1. Write what mixed numbers the pictures illustrate.

 a.  
   c.   

2. Draw pictures to illustrate these mixed numbers.

a.  4

2

3
 
c.  3

2

6
 
e.  6

8

10


Mixed numbers on a number line

3. Write the mixed number illustrated on each number line.

a.

  

b. (available in the book)

 

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

a. b. c. d.

 
5. Indicate the following mixed numbers on the number line. (available in the book)        

 

6. a. Indicate 2

3

5

  on the number line.   b. Write the mixed number that is  

4

5

  to its right.

 

    c. (available in the book)


Changing mixed numbers to fractions

To write 3

3

4

  as a fraction, count how many fourths there are:
  • Each pie has four fourths, so altogether there are 3 × 4 = 12 fourths.
  • Additionally there are three fourths.
  • The total is 15 fourths or 15/4.
   
    

Shortcut:        

Numerator: 3 × 4 + 3 = 15

Denominator: 4
     =  

15

4

Multiply the whole number times the denominator, then add the numerator. The result gives you
the amount of fourths, or the numerator for the fraction. The denominator will be the same.

7. Write as mixed numbers and as fractions.

a.   1

2

5

  =

     

5


d.        =

 

8. Marsha wrote 5

9

13

  as a fraction, and explained why 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. All total we get ____ slices, and each one is 13th part. So the fraction is 

 .

9. Write as fractions. Think of the shortcut.

   a.  7

1

2
   e.  2

5

11


Changing fractions to mixed numbers

To write a fraction, such as

58

7

 , as a mixed number, you need to find out
  • How many whole "pies" there are, and
  • How many slices are left over.
In the case of 

58

7

 , each whole "pie" will have 7 sevenths (how do you know?). So we ask:
  • How many 7s are there in 58?  (Those make the whole pies!)
  • After the 7s are gone, what is left over?

All 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.

To write that as a fraction, we get  

58

7

  = 8

2

7

 .
Example:  

45

4

  is the same as 45 ÷ 4, and 45 ÷ 4 = 11 R1. So, we get 11 whole pies and
1 fourth-part or slice left over. Writing that as a mixed number, 

45

4

  = 11

1

4

 .

The Shortcut: Think of the fraction line as a division symbol, and DIVIDE. The quotient tells
you the whole number part, and the remainder tells you the numerator of the fractional part.

10. Write the division problems with remainders as problems of "fractions changing to mixed numbers".

   a. 47 ÷ 4 = 11 R3

   

47

4

  =  11

3

4

   d. 35 ÷ 6 = ___ R ___

 

 =      

11. Write as mixed numbers or whole numbers.

a. 

62

8
b. 

16

3
c. 

27

5
d. 

32

9
e. 

7

2
i. 

24

11

 

Next lesson: adding like fractions

The ideas in this fraction lesson are taken from Math Mammoth Fractions 1 book. Only a few examples of each problem type are shown; you should make more problems of each kind for the student.

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