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The Connection Between Division and Multiplication

This is a complete lesson with teaching and exercises about the relationship between multiplication and division, meant for third grade. They are opposite operations, and both have to do with groups of equal size. Students write multiplication and division sentences from the same picture. In the later exercises, they write a division fact that matches the given multiplication, and vice versa. Lastly, students use their knowledge of multiplication facts to solve division problems.


We get both
a multiplication fact
and a division fact
from the same picture:
Three groups of 4 makes 12. 3 × 4 = 12



12 divided into groups of 4 is three groups.

12 ÷ 4 = 3
Multiplication and division are very closely related. They are opposite operations.
You could say division is “backwards” multiplication. 

1. Fill in the blanks.

 a.  Two groups of 6 is 12.

2 × 6 = 12



12 divided into groups of 6 is two groups.

12 ÷ 6 = 2

b.  Five groups of 2 is _____.

____ × 2 = ____






____ divided into groups of 2
is ___ groups.

_____ ÷ 2 = ____

c.  One group of 4 is 4.

____ × 4 = ____

4 divided into groups of 4 is one group.

_____ ÷ 4 = ____

d.  ____ groups of 3 is _____.

____ × ____ = ____

___ divided into groups of 3
is ___ groups.

_____ ÷____ = ____

e.  Five groups of 1 is 5.

____ × 1 = ____

5 divided into groups of 1
is ____ groups.

_____ ÷ 1 = ____

f.   ____ groups of ____ is _____.

____ × ____ = ____








___ divided into groups of 2
is ___ groups.

_____ ÷____ = ____



2. Make groups. Then write the division and multiplication facts that the pictures illustrate.

a.  Make groups of four.

____ × 4 =  8

8 ÷ 4 = ____



b.  Make groups of two.

____ × 2 = _____

_____ ÷ 2 = ____



c.  Make groups of four.

    ____ × 4 = _____

    _____ ÷ 4 = ____




 d.  Make groups of six.

____ × 6 =  _____

_____ ÷ 6 = ____

   
   
   
   

e.




____ × 4 = _____

_____ ÷ 4 = ____

f.   
   
   
 

____ × 7 = _____

_____ ÷ 7 = ____

g.

____ × 6 = ____

____ ÷ 6 = ____






h.

 


 
____ × 2 = ____

____ ÷ 2 = ____

i.

 
 
 
 
 

 
____ × 5 = ____

____ ÷ 5 = ____

3. Now draw sticks or circles and make a picture yourself. Write the division
    and multiplication sentences.

a.  Draw 15 sticks.
     Make groups of 5.
 

_____ ×  5  = _______

_______ ÷  5  =  _____

b.  Draw 24 sticks.
     Make groups of 8.
 

_____ × ____ = _______

______ ÷ ____ =  _____

c.  Draw 30 sticks.
     Make groups of 5.
 

_____ × ____ = _______

______ ÷ ____ =  _____

d.  Draw 27 sticks.
     Make groups of 9.
 

_____ × ____ = _______

_______ ÷ ____ =  _____

c.  Draw 32 sticks.
     Make groups of 16.
 

_____ × ____ = _______

_______ ÷ ____ =  _____

f.  Draw 16 sticks.
     Make groups of 2.
 

_____ × ____ = _______

_______ ÷ ____ =  _____

g.  Draw 8 sticks.
     Make a group of 8.
 

_____ × ____ = _______

_______ ÷ ____ =  _____

h.  Draw 18 sticks.
     Make groups of 9.
 

_____ × ____ = _______

_______ ÷ ____ =  _____

i.  Draw 20 sticks.
     Make groups of 5.
 

_____ × ____ = _______

_______ ÷ ____ =  _____

4. For each multiplication fact, write also a division fact. Think about the groups!

a.  7 × 2 = _____

______ ÷ 2 = _____

b.  12 × 2 = _____

______ ÷ 2 = _____

c.  8 × 5 = _____

______ ÷ 5 = _____

d.  6 × 7 = _____

______ ÷ ____ = _____

e.  7 × 7 = _____

______ ÷ ____ = _____  

f.  11 × 3 = _____

______ ÷ ____ = _____

g.  9 × 8 = _____

______ ÷ ____ = _____

h.  1 × 5 = _____

______ ÷ ____ = _____ 

i. 7 × 9 = _____

______ ÷ ____ = _____



You can solve a division problem by thinking of the matching multiplication.

30 ÷ 6 = ___       Think: what times 6 is 30?

___  × 6 = 30

So, since you already know the multiplication tables, division will be easy!

5. For each division, think of the corresponding multiplication and solve.

a.  14 ÷ 2 = ______

    ____ × 2 = 14

b.  18 ÷ 2 = ______

    ____ × 2 = ______

c.  21 ÷ 7 = ______

    ____ × 7 = ______

d.  54 ÷ 6 = ______

   ____ × ____ = ______

e.  24 ÷ 4 = ______

  ____ × ____ = ______  

f.  30 ÷ 3 = ______

  ____ × ____ = ______  

g.  32 ÷ 4 = ______

   ____ × ____ = ______ 

h.  56 ÷ 7 = ______

   ____ × ____ = ______

i.  55 ÷ 5 = ______

   ____ × ____ = ______ 

6. Divide. Again think of the multiplication.

a. b. c. d.

24 ÷ 4 = ______

16 ÷ 2 = ______

20 ÷ 2 = ______

36 ÷ 9 = ______

15 ÷ 5 = ______

35 ÷ 5 = ______

49 ÷ 7 = ______

54 ÷ 9 = ______

32 ÷ 8 = ______

40 ÷ 8 = ______

50 ÷ 5 = ______

42 ÷ 6 = ______

48 ÷ 6 = ______

56 ÷ 8 = ______

81 ÷ 9 = ______

100 ÷ 10 = _____

 

   Think of multiplication, and solve.
 

a.  1,000 ÷ 100 = ______  b.  400 ÷ 50 = ______   c.  200 ÷ 4 = ______  
     
d.  1,000 ÷ 500 = ______   e.  800 ÷ 800 = ______    f.  200 ÷ 40 = ______  



This lesson is taken from my book Math Mammoth Division 1.

Math Mammoth Division 1

A self-teaching worktext for 3rd grade that covers division concept, division & multiplication fact families, word problems, division facts, remainder, zero and one in division, and more.Download ($3.70). Also available as a printed copy.

=> Learn more and see the free samples!

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