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