Let's look at some properties of real number. For example, which real number
property justifies each of these four statements? Well, let's first recall some
properties of real numbers. And we are assuming here that all of the variables,
both in the example as well as in the table, represent real numbers. Let's look
at this first statement here. five (ab) = (5a) b. It turns out that the property
that's being illustrated here is the associative property for the operation of
multiplication. It's this property here. So let's write that. Associative property
for the operation of multiplication, and we'll just write the little multiplication
symbol here. Now often, when students are learning these properties, they confuse
associativity with commutativity. With the commutative property, we flip or reverse
the order. So the commutative property for the operation of multiplication might be
something like this. six nine = nine six.
Notice we are flipping or reversing the order of the multiplication. Think of a
commuter going back and forth to school. Whereas, with the associative property of
multiplication, we're either associating the a with the b first, or the a with the
five first and the result is the same. Alright, what about this second statement
here? four + r = r + four. This is demonstrating the commutative
property for the operation of addition. It's this property here. Notice we are
flipping or reversing the order of the addition. So, this is the communative
property for the operation of addition, and I'll put the little plus here.
Alright, what about this third statement here? 3u + 7u = (three+7) u. This is
demonstrating the distributive property down here, but notice that are statement
is starting on the right, and then going to the left. But that's okay, because
equal works in both directions. So, this third one is the distributive property.
Alright. And what about this last statement down here? (m+n) zero = zero.
Now remember, that m and n are both real number, which means m+n is also a real
number. So this is demonstrating this mu ltiplication property of zero down here,
where m + n = x. So this last statement is illustrating the multiplication property
of zero. And this is how we demonstrate some real number properties. Thank you,
and we'll see you next time.