State the name of the property illustrated. 6+(−4)=(−4)+6

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Identify the property being illustrated by the equation $6 + (-4) = (-4) + 6$.

Notice that the equation shows two numbers being added in different orders: first $6$ then $-4$, and then $-4$ then $6$.

Recall that the property which states that changing the order of addition does not change the sum is called the Commutative Property of Addition.

Confirm that the equation fits this property because the sum remains the same regardless of the order of the addends.

Therefore, the name of the property illustrated by $6 + (-4) = (-4) + 6$ is the Commutative Property of Addition.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Commutative Property of Addition

This property states that changing the order of the numbers in an addition operation does not change the sum. For example, a + b = b + a. In the given expression, 6 + (−4) = (−4) + 6, the order of the addends is switched, illustrating this property.

Additive Inverse

The additive inverse of a number is the number that, when added to the original number, results in zero. For example, the additive inverse of 4 is −4. Recognizing negative numbers as additive inverses helps understand expressions involving subtraction or negative terms.

Properties of Real Numbers

Real numbers follow specific properties such as commutative, associative, and distributive properties that govern arithmetic operations. Understanding these properties allows manipulation and simplification of expressions systematically and correctly.

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