which property justifies this statement

q+(r+s)=(q+r)+s

a. communicative property of addition
B. distributive property
C. Associative property of addition
D. identity property

C

I hope you were just looking for confirmation of your answer. Otherwise the question reveals a woeful lack of attention to your textbook.

The property that justifies the statement "q + (r + s) = (q + r) + s" is the Associative Property of Addition.

To understand why, let's break down the properties mentioned:

A. Communicative Property of Addition:
This property states that changing the order of the numbers being added does not change the result. For example, with the communicative property, you can reorganize "q + r" to "r + q" without changing the sum. However, in the given statement, the order of addition remains unchanged, so the communicative property is not applicable.

B. Distributive Property:
The distributive property is usually expressed as "a × (b + c) = (a × b) + (a × c)" and involves multiplication and addition. Since the given statement only involves addition, the distributive property is not applicable here.

C. Associative Property of Addition:
This property states that the grouping of numbers being added together does not affect the sum. In other words, you can freely change the grouping of the numbers without changing the result. In the statement "q + (r + s) = (q + r) + s," you can see that we have "q + (r + s)" on the left side and "(q + r) + s" on the right side. By rearranging the grouping of q, r, and s, the sum remains the same. Therefore, the Associative Property of Addition justifies this statement.

D. Identity Property:
The identity property states that adding zero to any number does not change the value of that number. However, in the given statement, there is no reference to zero. Hence, the identity property is not applicable in this case.

In conclusion, the correct answer is C. Associative Property of Addition.