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: 


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 _____ ÷ 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 _____ ÷____ = ____ 

e.
Five groups of 1 is 5.
____ × 1 = ____ 5 divided into groups of 1 _____ ÷ 1 = ____ 
f. ____ groups of ____ is _____.
____ × ____ = ____ ___ divided into groups of 2 _____ ÷____ = ____ 
2. Make groups. Then write the division and multiplication facts that the pictures illustrate.











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











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.
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.

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