### Video Transcript

Which equation shows the
associative property of addition? Is it (A) a half plus negative a
half equals zero? (B) One-half plus two-thirds equals
two-thirds plus one-half. Is it (C) one-half plus two-thirds
equals seven-sixths? (D) One-half plus two-thirds plus
three-quarters equals one-half plus two-thirds plus three-quarters. Or (E) two-thirds plus zero equals
two-thirds.

Remember, the associative property
of addition says that the sum of three or more numbers remains the same regardless
of how the numbers are grouped. So, we’re going to go through each
of our equations and identify which of these satisfies the associative property. We’re going to disregard (A)
immediately. (A), in fact, is showing us an
example of the additive inverse. The additive inverse of one-half is
negative one-half because the result is zero when we add them. And what about (B)? Well, no, the associative property
does tell us we can perform the addition in any order but that there are going to be
three or more numbers, and it’s regardless of how those three or more numbers are
grouped. So (B) does not show the
associative property. (C) just gives us an equation. It tells us that a half plus
two-thirds equals seven-sixths, and so it’s not (C).

So, what about (D)? We do indeed have three numbers on
each side of our equation, and they’re grouped differently on both sides. Otherwise though, the numbers
remain unchanged. So, yes, (D) does show the
associative property of addition. If we perform a half plus
two-thirds first and then add three-quarters, that’s the same as adding a half to
the result of two-thirds plus three-quarters. And so the answer is (D). (D) shows the associative property
of addition. We can see quite clearly it’s not
(E). That’s just showing us that when we
add zero to a number, it remains unchanged.