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

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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)

q = 0 + q

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(B)

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

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(C)

q + r = r + q

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(D)

q = r + s + t

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 $q = 0 + q$ . This does not show the associative property; it shows that adding zero to a number gives the number itself, which is the identity property of addition.
Analyzing Choice (B): Analyze choice (B) to see if it demonstrates the associative property. $\newline$ Choice (B) is $q + (r + s) = (q + r) + s$ . This equation is in the form of the associative property, where the grouping of addends is changed without changing the sum.
Analyzing Choice (C): Analyze choice (C) to see if it demonstrates the associative property. Choice (C) is $q + r = r + q$ . This does not show the associative property; it shows the commutative property of addition, which states that the order of addends can be changed without changing the sum.
Analyzing Choice (D): Analyze choice (D) to see if it demonstrates the associative property. Choice (D) is $q = r + s + t$ . This does not show the associative property; it is simply an equation with three addends added together without any grouping to indicate the associative property.
Select Correct Answer: Select the correct answer based on the analysis. $\newline$ From the analysis in the previous steps, choice (B) $q + (r + s) = (q + r) + s$ is the only one that demonstrates the associative property of addition.