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Name the addition property illustrated by each of the following examples:

[tex]\[
\begin{array}{l}
A + (B + C) = (A + B) + C \quad \text{Associative Property} \\
A + B = B + A \quad \text{Commutative Property} \\
A + (-A) = 0 \quad \text{Inverse Property} \\
A + 0 = A \quad \text{Identity Property}
\end{array}
\][/tex]



Answer :

GinnyAnswer
Sure, let's identify the addition properties illustrated by each of the given examples:

1. Associative Property:
[tex]\[ A + (B + C) = (A + B) + C \][/tex]
This property states that the way in which numbers are grouped when being added does not change their sum. It focuses on the grouping of the numbers.

2. Commutative Property:
[tex]\[ A + B = B + A \][/tex]
This property indicates that the order in which two numbers are added does not affect their sum. It emphasizes the interchangeability of the numbers' positions.

3. Additive Inverse Property:
[tex]\[ A + (-A) = 0 \][/tex]
This property states that any number plus its additive inverse (or opposite) equals zero. This illustrates the concept of zero being the identity element for addition – fundamentally, this shows the balance of a number and its negation.

4. Additive Identity Property:
[tex]\[ A + 0 = A \][/tex]
This property states that any number plus zero is the number itself. Here, zero is known as the additive identity, highlighting that adding zero leaves the original number unchanged.

To summarize, the properties illustrated by each example are:

1. Associative Property
2. Commutative Property
3. Additive Inverse Property
4. Additive Identity Property