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

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Full solution

Q. Which equation shows the associative property of addition?\newlineChoices:\newline(A) q=r+s+tq = r + s + t\newline(B) q+r=s+tq + r = s + t\newline(C) q+(r+s)=(q+r)+sq + (r + s) = (q + r) + s\newline(D) q=0+qq = 0 + q
  1. Property Explanation: The associative property of addition states that the way in which addends are grouped does not change the sum. The mathematical expression of this property is a + b) + c = a + (b + c)\.
  2. Step \(1: Examine each choice to see if it matches the associative property of addition:\newline(A) q=r+s+tq = r + s + t does not show any grouping of addends, so it does not demonstrate the associative property.
  3. Step 22: (B) q+r=s+tq + r = s + t is an equation showing equality but does not involve changing the grouping of addends, so it does not demonstrate the associative property.
  4. Step 33: (C) q+(r+s)=(q+r)+sq + (r + s) = (q + r) + s shows a change in the grouping of addends without changing the sum, which is exactly what the associative property of addition describes.
  5. Step 44: (D) q=0+qq = 0 + q is an example of the identity property of addition, not the associative property.
  6. Step 44: (D) q=0+qq = 0 + q is an example of the identity property of addition, not the associative property.Therefore, the correct choice that shows the associative property of addition is (C) q+(r+s)=(q+r)+sq + (r + s) = (q + r) + s.

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