In Exercises 75–84, state the name of the property illustrated. 6+(−4)=(−4)+6

Verified step by step guidance

1. Identify the operation being used in the expression: addition.
2. Observe the order of the numbers in the expression: \(6 + (-4)\) and \((-4) + 6\).
3. Notice that the numbers are the same, but their order is reversed.
4. Recall the property of addition that states changing the order of the numbers does not change the sum.
5. This property is known as the Commutative Property of Addition.

Key Concepts

Commutative Property of Addition

The Commutative Property of Addition states that the order in which two numbers are added does not affect the sum. This means that for any two numbers a and b, a + b = b + a. In the given equation, 6 + (−4) = (−4) + 6 illustrates this property, as both expressions yield the same result.

Associative Property of Addition

The Associative Property of Addition indicates that the way in which numbers are grouped in an addition operation does not change the sum. For example, (a + b) + c = a + (b + c). While not directly illustrated in the provided equation, understanding this property helps in recognizing how addition can be rearranged without altering the outcome.

Identity Element of Addition

The Identity Element of Addition refers to the number that, when added to any number, does not change the value of that number. The identity element for addition is 0, as a + 0 = a for any number a. This concept is foundational in understanding how addition operates within the set of real numbers, complementing the properties illustrated in the question.