-
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a plus b times open
parentheses c plus d is
-
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
-
represents the associative
property of addition?
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So remember,
associative property--
-
we're talking about
it doesn't matter
-
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,
-
if we associate b plus c
first or a plus b first.
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So this is the associative
property of addition.
-
Let's do-- which one of
the equations on the right
-
represents the
distributive property
-
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,
-
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
-
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
-
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.