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Which equation shows the commutative property of addition?\newlineChoices:\newline(A) k+m=m+kk + m = m + k\newline(B) k+(m+n)=(k+m)+nk + (m + n) = (k + m) + n\newline(C) k+m=m+nk + m = m + n\newline(D) k+0=kk + 0 = k

Full solution

Q. Which equation shows the commutative property of addition?\newlineChoices:\newline(A) k+m=m+kk + m = m + k\newline(B) k+(m+n)=(k+m)+nk + (m + n) = (k + m) + n\newline(C) k+m=m+nk + m = m + n\newline(D) k+0=kk + 0 = k
  1. Understand Commutative Property: Understand the commutative property of addition. The commutative property of addition states that the order in which two numbers are added does not change the sum. In other words, a+b=b+aa + b = b + a.
  2. Match Given Choices: Match the given choices with the commutative property.\newlineWe need to find an equation that shows the order of addition can be changed without affecting the sum. This means we are looking for an equation of the form a+b=b+aa + b = b + a.
  3. Evaluate Choices Given: Evaluate the choices given.\newline(A) k+m=m+kk + m = m + k - This choice shows two variables being added in both orders, which matches the commutative property.\newline(B) k+(m+n)=(k+m)+nk + (m + n) = (k + m) + n - This choice shows the associative property, not the commutative property.\newline(C) k+m=m+nk + m = m + n - This choice does not show the commutative property because it implies a potential change in value (nn is not necessarily equal to kk).\newline(D) k+0=kk + 0 = k - This choice shows the identity property of addition, not the commutative property.
  4. Select Correct Answer: Select the correct answer.\newlineFrom the evaluation in Step 33, we can see that choice (A) k+m=m+kk + m = m + k correctly represents the commutative property of addition.

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