Which equation shows the associative property of addition? $\newline$ Choices: $\newline$ (A) $p = p + 0$ $\newline$ (B) $(p + q) + r = p + (q + r)$ $\newline$ (C) $p + q = q + r$ $\newline$ (D) $q + p = p + q$

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Grade 6

Properties of addition

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Q. Which equation shows the associative property of addition?

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Choices:

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(A)

p = p + 0

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(B)

(p + q) + r = p + (q + r)

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(C)

p + q = q + r

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(D)

q + p = p + q

Understand Associative Property: Understand the associative property of addition. The associative property of addition states that the way in which addends are grouped does not change the sum. In mathematical terms, this property is expressed as $(a + b) + c = a + (b + c)$ .
Analyzing Choice (A): Analyze choice (A) to see if it demonstrates the associative property. $\newline$ Choice (A) is $p = p + 0$ . This equation represents the identity property of addition, which states that adding zero to a number does not change its value. This does not show the associative property.
Analyzing Choice (B): Analyze choice (B) to see if it demonstrates the associative property. $\newline$ Choice (B) is $(p + q) + r = p + (q + r)$ . This equation is in the form of the associative property of addition, where the grouping of addends is changed but the sum remains the same.
Analyzing Choice (C): Analyze choice (C) to see if it demonstrates the associative property. Choice (C) is $p + q = q + r$ . This equation does not show the associative property; instead, it suggests a relationship between $p$ , $q$ , and $r$ that is not relevant to the associative property.
Analyzing Choice (D): Analyze choice (D) to see if it demonstrates the associative property. Choice (D) is $q + p = p + q$ . This equation represents the commutative property of addition, which states that the order of addends can be changed without affecting the sum. This does not show the associative property.
Select Correct Answer: Select the correct answer based on the analysis. $\newline$ From the previous steps, we can see that choice (B) correctly demonstrates the associative property of addition. Therefore, the correct answer is (B) $(p + q) + r = p + (q + r)$ .