Definitions
Any number multiplied by zero has a product of zero.
The Zero Property
Name the property being used and solve!
7 x 4 = 4 x 7
commutative property
28
Solve the problem and name the property you used: 1 x 1,398,610
Identity Property
1,398,610
8 x 3 = 3 x 8
24 = 24
Multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products.
Distributive Property
Name the property and solve.
(3 x 2) x 5 = 3 x (2 x 5)
Associative Property
30
Use the Associative Property to rewrite this equation:
(3 x 5) x 10
3 x (5 x 10)
(5 x 9) x 0 = 5 x (9 x 0)
0 = 0
This property states that factors can be multiplied in any order and the product is always the same. This also called the order property of multiplication.
Commutative Property
Name the property. Solve.
81 x 1
Identity Property
81
Use the commutative property to rewrite this equation and solve.
5 x 6
6 x 5 = 30
4(3 + 4) = (4 x 3) + (4 x 4)
28 = 28
Any number multiplied by 1 remains the same
Identity Property
It is the property where you distribute a larger number into 2 smaller numbers.
6 x 7 = 6 x (5 + 2)
6 x 7 = (6 x 5) + (6 x 2)
Distributive Property
Use the distributive property to solve.
3 x 9
3 x 9 = 3 x (5 + 4)
3 x 9 = (3 x 5 ) + (3 x 4)
3 x 9 = 15 + 12
3 x 9 = 27
2 x (8 x 3) = (2 x 8) x 3
48 = 48
When the grouping of factors is changed, the product stays the same.
Associative Property
Name the property and solve
8 x (3+9) = (8x3) + (8x9)
Distributive Property
96
9 x (2 x 3) = (9 x 2) x 3
Associative Property
54
5(4 x 6) = (5 x 4)6
120 = 120