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Which equation shows the associative property of addition?\newlineChoices:\newline(A) u+v=v+wu + v = v + w\newline(B) u+(v+w)=(u+v)+wu + (v + w) = (u + v) + w\newline(C) 0+u=u0 + u = u\newline(D) u+v=v+uu + v = v + u

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Q. Which equation shows the associative property of addition?\newlineChoices:\newline(A) u+v=v+wu + v = v + w\newline(B) u+(v+w)=(u+v)+wu + (v + w) = (u + v) + w\newline(C) 0+u=u0 + u = u\newline(D) u+v=v+uu + v = v + u
  1. 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)(a + b) + c = a + (b + c).
  2. Analyze Given Choices: Analyze the given choices to identify which one represents the associative property of addition. We need to find an equation that shows the grouping of addends can be changed without affecting the sum.
  3. Evaluate Choice (A): Evaluate choice (A) u+v=v+wu + v = v + w. This equation does not show the associative property; it suggests commutativity, which is not what we are looking for.
  4. Evaluate Choice (B): Evaluate choice (B) u+(v+w)=(u+v)+wu + (v + w) = (u + v) + w. This equation matches the form of the associative property of addition, where the grouping of addends is changed without affecting the sum.
  5. Evaluate Choice (C): Evaluate choice (C) 0+u=u0 + u = u. This equation represents the identity property of addition, not the associative property.
  6. Evaluate Choice (D): Evaluate choice (D) u+v=v+uu + v = v + u. This equation represents the commutative property of addition, not the associative property.
  7. Select Correct Answer: Select the correct answer based on the evaluations.\newlineFrom the analysis, we can see that choice (B) u+(v+w)=(u+v)+wu + (v + w) = (u + v) + w is the only equation that demonstrates the associative property of addition.

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