Video Transcript
What property of addition is
demonstrated by two over nine plus four over nine equals four over nine plus two
over nine?
In this question, we need to
determine which property of addition is represented by the given identity. To do this, we first need to look
at the given identity. We can see that each side of the
identity involves the same two rational numbers. However, the order that we need to
add the numbers has been switched.
We can then recall that the
commutative property of the addition of rational numbers tells us that we can
reorder the sum of rational numbers without affecting the value. In other words, for any rational
numbers 𝑎 and 𝑏, 𝑎 plus 𝑏 is equal to 𝑏 plus 𝑎.
Since two over nine and four over
nine are both rational numbers as they are the quotient of integers, we can see that
the given identity is given by the commutative property with the value of 𝑎 equal
to two over nine and the value of 𝑏 equal to four over nine.
