What are the properties of addition?

Answer 1

There are 5 Properties:

CLOSURE-The sum of two integers is an integer.

EX. 5+9=14 (14 is an integer)

COMMUTATIVE-Changing the order of the addends does not change the sum.

EX. 8+4=4+8

ASSOCIATIVE-Changing the grouping of the addends does not change the sum.

EX. (-5+4)+6=-5+(4+6)

IDENTITY-The sum of an integer and zero equals the original integer.

EX. -2+0=0+(-2)=-2

INVERSE-The sum of any integer and its additive inverse equals zero, the identity element of addition.

EX. 6+(-6)=-6+6=0

* * * * *

Commutativity and associativity are properties of addition. The others are properties of the set over which addition is defined, not of addition itself.

Answer 2

Properties of Addition

Commutative : The commutative property in math comes from the words "move around." This rule states that you can move numbers or variables in algebra around and still get the same answer. This equation defines the commutative property of addition: a + b = b + a

Associative: To “associate” means to connect or join with something.

According to the associative property of addition, the sum of three or more numbers remains the same regardless of how the numbers are grouped.

Identify: Identity Property Of Addition :

The identity property of addition is that the sum of any number and its identity value gives the same number as the result. In addition, 0 is the identity element.

Distributive: The Distributive Property is easy to remember, if you recall that "multiplication distributes over addition". Formally, they write this property as "a(b + c) = ab + ac". In numbers, this means, for example, that 2(3 + 4) = 2×3 + 2×4. Any time they refer in a problem to using the Distributive Property, they want you to take something through the parentheses (or factor something out); any time a computation depends on multiplying through a parentheses (or factoring something out), they want you to say that the computation used the Distributive Property.

• Why is the following true? 2(x + y) = 2_x_ + 2_y_

Since they distributed through the parentheses, this is true by the Distributive Property.