Commutative Property
What is the Commutative Property of Addition?
The Commutative Property of Addition says you can add numbers in any order and get the same result.
Example: 4 + 5 = 5 + 4
What is the Associative Property of Addition?
The Associative Property of Addition means you can group numbers in any way when adding, and the sum will be the same.
Example: (2 + 3) + 4 = 2 + (3 + 4)
What is the Distributive Property?
The Distributive Property says you can multiply a number by a group of numbers added together by multiplying each separately and then adding the products.
Example: 3 × (2 + 4) = (3 × 2) + (3 × 4)
What is the Identity Property of Addition?
The Identity Property of Addition says that when you add 0 to any number, the sum is that number.
Example: 7 + 0 = 7
True or False: The Commutative Property also works for multiplication.
True.
Example: 3 × 7 = 7 × 3
True or False: The Associative Property works for multiplication too.
True.
Example: (5 × 3) × 2 = 5 × (3 × 2)
Solve using the Distributive Property: 5 × (3 + 2)
(5 × 3) + (5 × 2) = 15 + 10 = 25
What is the Identity Property of Multiplication?
The Identity Property of Multiplication says that when you multiply any number by 1, the product is that number.
Example: 9 × 1 = 9
Using the Commutative Property, what is 8 × 12?
12 × 8, which is 96.
Using the Associative Property, simplify (4 × 6) × 2.
4 × (6 × 2) = 4 × 12 = 48
Apply the Distributive Property to solve: 6 × (4 + 7)
(6 × 4) + (6 × 7) = 24 + 42 = 66
Solve using the Identity Property: 15 + 0.
15 + 0 = 15
Show how the Commutative Property works for 6 + 9.
6 + 9 = 9 + 6, both equal 15.
Rearrange the numbers using the Associative Property to simplify: (8 + 5) + 9.
8 + (5 + 9) = 8 + 14 = 22
Use the Distributive Property to break down: 9 × (5 + 6
(9 × 5) + (9 × 6) = 45 + 54 = 99
Apply the Identity Property of Multiplication to solve: 14 × 1.
14 × 1 = 14
Apply the Commutative Property to solve 14 × 5.
5 × 14, which is 70.
Solve using the Associative Property: (7 × 2) × 3.
7 × (2 × 3) = 7 × 6 = 42
Solve using the Distributive Property: 8 × (3 + 9)
(8 × 3) + (8 × 9) = 24 + 72 = 96
True or False: The Identity Property works the same for both addition and multiplication.
False.
Explanation: For addition, the identity is 0, and for multiplication, the identity is 1.