associative property of multiplication...the associative property of multiplication states that the...
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Name: ____________________________
Associative Property of Multiplication
The Associative Property of Multiplication states that the product of a set of
numbers is the same, no matter how they are grouped.
example: (2 x 3) x 4 = 2 x (3 x 4)
6 x 4 = 2 x 12
24 = 24
Find the products for each. First solve the part in parenthesis and write a new
multiplication fact on the first line. Then write the product on the bottom line.
a. (4 x 2) x 6 = 4 x (2 x 6) b. (2 x 5) x 3 = 2 x (5 x 3)
_________ = _________ _________ = _________
_________ = _________ _________ = _________
c. (4 x 5) x 2 = 4 x (5 x 2) d. (4 x 7) x 1 = 4 x (7 x 1)
_________ = _________ _________ = _________
_________ = _________ _________ = _________
e. (6 x 2) x 5 = 6 x (2 x 5) f. (3 x 3) x 4 = 3 x (3 x 4)
_________ = _________ _________ = _________
_________ = _________ _________ = _________
g. (3 x 2) x 2 = 3 x (2 x 2) (2 x 2) x (4 x 1) = 2 x (2 x 4) x 1
_________ = _________ _________ = _________
_________ = _________ _________ = _________
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Name: Date:
Cute Lion4x5 4x4 6x2 3x6 6x3 4x4 7x2 2x10 3x4 5x3 2x8 2x7 2x9 6x3 3x6 5x4 8x2 7x2 5x4
8x2 10x2 3x5 10x2 6x1 9x2 7x1 2x10 2x2 2x6 1x1 6x3 2x3 8x2 5x2 5x4 5x4 7x2 4x4
4x5 6x2 5x3 1x5 1x9 1x3 1x4 1x2 5x1 1x8 2x3 1x1 2x1 3x2 6x1 4x1 2x10 2x7 7x2
2x10 2x10 1x10 3x2 2x4 2x2 6x1 2x3 9x1 1x4 4x1 1x1 7x1 4x2 1x10 2x4 10x1 3x5 5x3
10x2 2x7 2x7 9x1 10x1 0x0 5x0 0x1 7x0 3x0 0x4 0x6 0x8 0x3 1x7 3x2 5x4 2x8 7x2
4x3 6x3 9x1 1x5 1x4 0x1 1x9 7x0 0x0 0x5 0x7 1x0 1x6 8x0 1x4 4x2 5x2 3x5 7x2
2x10 9x2 8x2 4x1 8x1 0x0 10x1 0x8 1x6 5x2 2x1 3x0 4x2 0x1 3x1 1x10 4x5 3x5 6x2
6x2 3x4 1x6 4x1 2x4 0x2 4x0 7x0 5x9 3x1 4x9 1x0 5x0 0x1 5x1 3x2 2x4 5x4 3x4
7x2 7x2 2x7 1x7 6x1 0x1 0x9 10x5 5x10 6x7 7x7 8x6 8x0 3x0 2x4 1x1 5x3 5x3 8x2
2x9 2x7 1x7 2x1 4x1 4x0 0x3 8x5 5x7 5x9 4x10 7x6 9x0 10x0 7x1 2x3 1x1 6x3 4x4
2x9 10x2 2x7 1x7 1x1 3x2 1x7 1x5 8x1 2x2 5x2 4x2 2x4 1x5 6x1 2x2 10x2 3x4 3x4
6x3 3x4 9x1 2x3 1x5 1x8 4x1 1x9 1x1 2x4 5x2 1x1 2x1 10x1 1x5 1x8 2x3 7x2 2x10
2x7 2x10 4x4 1x4 5x3 4x1 9x2 0x3 0x9 0x2 0x5 2x0 3x5 5x1 4x5 5x1 2x7 6x3 3x4
7x1 4x4 6x3 5x4 2x10 2x8 4x0 5x0 0x8 6x6 1x0 10x0 10x0 10x2 2x8 10x2 6x2 2x7 6x3
4x2 6x3 2x9 2x8 5x3 7x2 8x0 0x3 5x10 6x6 5x9 0x8 0x1 3x4 4x4 2x7 6x3 4x3 2x8
0x10 6x4 7x3 3x8 0x10 0x8 5x0 9x0 4x8 8x4 4x9 0x9 9x3 4x6 3x7 6x5 4x7 4x6 5x5
0x5 8x0 0x9 0x4 0x10 3x9 2x0 0x2 10x0 7x5 1x0 0x8 10x3 7x4 9x3 6x5 6x5 3x8 5x5
6x4 9x3 8x3 7x3 10x3 3x8 10x3 0x1 9x0 0x9 0x9 0x1 0x2 3x8 6x4 4x6 8x3 6x5 7x4
10x3 9x3 5x6 8x3 7x4 4x6 8x3 5x5 5x6 7x4 7x4 7x4 10x3 7x3 6x5 6x4 8x3 3x7 3x10
8x3 3x8 8x3 5x5 3x10 3x10 4x7 3x7 5x6 6x4 5x6 6x4 4x6 3x9 10x3 4x6 5x6 5x5 6x4
Key:0 Orange1‐10 Brown11‐20 Blue21‐30 Green31‐50 Tan
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ANSWER KEY
Associative Property of Multiplication
The Associative Property of Multiplication states that the product of a set of
numbers is the same, no matter how they are grouped.
example: (2 x 3) x 4 = 2 x (3 x 4)
6 x 4 = 2 x 12
24 = 24
Find the products for each. First solve the part in parenthesis and write a new
multiplication fact on the first line. Then write the product on the bottom line.
a. (4 x 2) x 6 = 4 x (2 x 6) b. (2 x 5) x 3 = 2 x (5 x 3)
8 x 6 = 4 x 12 10 x 3 = 2 x 15
48 = 48 30 = 30
c. (4 x 5) x 2 = 4 x (5 x 2) d. (4 x 7) x 1 = 4 x (7 x 1)
20 x 2 = 4 x 10 28 x 1 = 4 x 7
40 = 40 28 = 28
e. (6 x 2) x 5 = 6 x (2 x 5) f. (3 x 3) x 4 = 3 x (3 x 4)
12 x 5 = 6 x 10 9 x 4 = 3 x 12
60 = 60 36 = 36
g. (3 x 2) x 2 = 3 x (2 x 2) (2 x 2) x (4 x 1) = 2 x (2 x 4) x 1
6 x 2 = 3 x 4 4 x 4 = 2 x 8 x 1
12 = 12 16 = 16
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Name: ____________________________
Distributive Property of Multiplication
The Distributive Property of Multiplication is used when we divide a
multiplication array into two parts, making two smaller multiplication facts.
When you add to find the sum of the two smaller products, you have the
amount of the original array.
This array shows 3 x 5 The array was broken into two smaller
parts. It shows 3 x 3 = 9 and 3 x 2 = 6.
What is 3 x 5? What is 9 + 6? __________
3 x 5 = __________ What is 3 x (3 + 2)? __________
The array above shows the multiplication fact _______ x _______ = _______ .
Now the array shows two facts.
The facts are _______ x _______ = _______ and _______ x _______ = _______ .
Add to find the sum of the two products. Your answer is _______.
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The array above shows the multiplication fact _______ x _______ = _______ .
Now the array shows two facts.
The facts are _______ x _______ = _______ and _______ x _______ = _______ .
Add to find the sum of the two products. Your answer is _______.
Make an array to show 3 x 8. Be sure your symbols are arranged in neat rows and
columns.
Now draw a dotted line on your illustration to divide the array into two arrays.
What two multiplication facts do you see?
_______ x _______ = _______ and _______ x _______ = _______
Add to find the sum of the two products. Your answer is _______.
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ANSWER KEY
Distributive Property of Multiplication
The Distributive Property of Multiplication is used when we divide a
multiplication array into two parts, making two smaller multiplication facts.
When you add to find the sum of the two smaller products, you have the
amount of the original array.
This array shows 3 x 5 The array was broken into two smaller
parts. It shows 3 x 3 = 9 and 3 x 2 = 6.
What is 3 x 5? What is 9 + 6? 15
3 x 5 = 15 What is 3 x ( 3 + 2)? 15
The array above shows the multiplication fact 3 x 7 = 21 .
Now the array shows two facts.
The facts are 3 x 4 = 12 and 3 x 3 = 9 .
Add to find the sum of the two products. Your answer is 21.
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The array above shows the multiplication fact 4 x 12 = 48 .
Now the array shows two facts.
The facts are 4 x 6 = 24 and 4 x 6 = 24 .
Add to find the sum of the two products. Your answer is 48.
Make an array to show 3 x 8. Be sure your symbols are arranged in neat rows and
columns.
ANSWER WILL VARY - Students can divide the array in different areas,
which will result in different multiplication facts.
Now draw a dotted line on your illustration to divide the array into two arrays.
What two multiplication facts do you see?
3 x 4 = 12 and 3 x 4 = 12
Add to find the sum of the two products. Your answer is 24.
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