The commutative property of multiplication tells us that we can change the order of the factors in a multiplication problem and not change the product. The associative property of multiplication tells us that we can change the way we group three or more factors and not change the product.
Test Objectives:•Demonstrate the ability to identify the parts of a multiplication problem
•Demonstrate the ability to rewrite a product using the commutative and associative properties
•Demonstrate the ability to use the distributive property of multiplication to find a product
Properties of Multiplication Test:
#1:
Instructions: Multiply each and identify the parts of the multiplication problem.
a) 6 x 2
b) 7 x 2 x 1
c) 171 x 9 x 0 x 5 x 18
#2:
Instructions: Rewrite each using the commutative property of multiplication.
a) 3 x 7
b) 12 x 8
c) 6 x 7
d) 9 x 5
#3:
Instructions: Rewrite each using the associative property of multiplication.
a) (5 x 2) x 7
b) 8 x (1 x 3)
c) (10 x 4) x 2
d) (3 x 7) x 5
#4:
Instructions: Use the distributive property of multiplication to find each product.
a) 6(4 - 2)
b) 3(7 + 3)
c) 8(9 + 4)
d) 10(1 + 3)
#5:
Instructions: Use the distributive property of multiplication to find each product.
a) 3(5 - 3)
b) 10(7 - 7)
c) 8(5 + 2)
d) 11(4 + 1)
Written Solutions:
Solution:
a) 6 x 2 = 12 : 6 - factor, 2 - factor, 12 - product
b) 7 x 2 x 1 = 14 : 7 - factor, 2 - factor, 1 - factor, 14 - product
c) 171 x 9 x 0 x 5 x 18 = 0 : 171 - factor, 9 - factor, 0 - factor, 5 - factor, 18 - factor, 0 - product
Solution:
a) 3 x 7 = 7 x 3
b) 12 x 8 = 8 x 12
c) 6 x 7 = 7 x 6
d) 9 x 5 = 5 x 9
Solution:
a) (5 x 2) x 7 = 5 x (2 x 7)
b) 8 x (1 x 3) = (8 x 1) x 3
c) (10 x 4) x 2 = 10 x (4 x 2)
d) (3 x 7) x 5 = 3 x (7 x 5)
Solution:
a) 6(4 - 2) = 6 x 4 - 6 x 2 = 24 - 12 = 12
b) 3(7 + 3) = 3 x 7 + 3 x 3 = 21 + 9 = 30
c) 8(9 + 4) = 8 x 9 + 8 x 4 = 72 + 32 = 104
d) 10(1 + 3) = 10 x 1 + 10 x 3 = 10 + 30 = 40
Solution:
a) 3(5 - 3) = 3 x 5 - 3 x 3 = 15 - 9 = 6
b) 10(7 - 7) = 10 x 7 - 10 x 7 = 70 - 70 = 0
c) 8(5 + 2) = 8 x 5 + 8 x 2 = 40 + 16 = 56
d) 11(4 + 1) = 11 x 4 + 11 x 1 = 44 + 11 = 55