addition property of 0The sum of any number and 0 is equal to that number. The number 0 is often called the additive identity.
associative law of additionFor three or more numbers, the sum is the same regardless of how you group the numbers. For example, (6 + 2) + 1 = 6 + (2 + 1).
associative law of multiplication

For three or more numbers, the product is the same regardless of how you group the numbers. For example, 3 • (5 • 7) = 3 • (5 • 7).

commutative law of additionTwo numbers can be added in any order without changing the sum. For example, 6 + 4 = 4 + 6.
commutative law of multiplication

Two numbers can be multiplied in any order without changing the product. For example, 8 • 9 = 9 • 8.

multiplication property of 1The product of any number and 1 is equal to that number. The number 1 is often called the multiplicative identity.