WEBVTT

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a plus b times open
parentheses c plus d is

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equal to a plus bc plus
bd represents which

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of the following properties?

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So to get from the left-hand
side to the right-hand side,

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it looks like what they did
is they multiplied the b times

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the c plus d.

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In fact, they
distributed the b. b

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times c plus d is b
times c, plus b times d.

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So this is clearly the
distributive property.

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Let's do another one.

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4 plus open parentheses
10 plus 6, they're saying,

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is the same thing as 4
plus 10 first, plus 6.

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So on the left-hand side, we're
doing the 10 plus 6 first,

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and then we're adding the 4.

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On the right-hand side, we're
adding the 4 plus 10 first,

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and then we're adding the 6.

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And we're saying they're
equal to each other.

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It doesn't matter how we
associate these numbers.

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Here we're associating
the 10 and the 6 first,

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and then we're adding the 4.

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Here we're associating
the 4 and the 10 first,

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and then we're adding the 6.

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So this is the associative
property for addition.

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Let's do several more.

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a plus b is equal to b
plus a represents which

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of the following properties?

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So it doesn't matter
which order I'm adding.

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It doesn't matter if I
do a plus b or b plus a.

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This is the
commutative property.

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Do another one.

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Which one of the
equations on the right

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represents the associative
property of addition?

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So remember,
associative property--

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we're talking about
it doesn't matter

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how we associate the numbers.

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So we might do the operation
on two of the numbers first

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and then on the third, or on
maybe two of the other numbers

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and then on the one
that's left over.

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So let's see what over
here looks like that.

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So this right over here, this
is the commutative property.

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This right over here is
the distributive property.

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This one right over here--
on the left-hand side,

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we add b plus c first.

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On the right-hand side,
we add a plus b first.

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And these two things
are equal to each other.

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It doesn't matter
how we associate it,

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if we associate b plus c
first or a plus b first.

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So this is the associative
property of addition.

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Let's do-- which one of
the equations on the right

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represents the
distributive property

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of addition over multiplication?

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So let's see.

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This first one, they're just
changing the associations.

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Here, this is commutative,
this last one.

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Here, they're actually
distributing the b

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over the c plus d.

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So b times c plus d is the
same thing as bc plus bd.

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So it's that one
right over there.

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Maybe do a few more of this.

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This is a lot of fun.

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a plus b plus c is equal
to a plus b plus c,

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so this once again, they're
re-associating the numbers.

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But it doesn't matter which
order we associate them in.

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So this is the
associative property.

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Which one of the
equations on the right

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represents the commutative
property of addition?

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So commutative-- we don't
care about the order

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in which we're
doing the operation.

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So a plus b is
equal to b plus a.

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Which one of the
equations on the right

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represents the commutative
property of addition?

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Well, that's what
they just asked us.

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a plus b is equal to b plus a.

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And we are done.