a plus b times open
parentheses c plus d is

equal to a plus bc plus
bd represents which

of the following properties?

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

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

the c plus d.

In fact, they
distributed the b. b

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

So this is clearly the
distributive property.

Let's do another one.

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

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

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

and then we're adding the 4.

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

and then we're adding the 6.

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

It doesn't matter how we
associate these numbers.

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

and then we're adding the 4.

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

and then we're adding the 6.

So this is the associative
property for addition.

Let's do several more.

a plus b is equal to b
plus a represents which

of the following properties?

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

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

This is the
commutative property.

Do another one.

Which one of the
equations on the right

represents the associative
property of addition?

So remember,
associative property--

we're talking about
it doesn't matter

how we associate the numbers.

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

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

and then on the one
that's left over.

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

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

This right over here is
the distributive property.

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

we add b plus c first.

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

And these two things
are equal to each other.

It doesn't matter
how we associate it,

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

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?

So let's see.

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

Here, this is commutative,
this last one.

Here, they're actually
distributing the b

over the c plus d.

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

So it's that one
right over there.

Maybe do a few more of this.

This is a lot of fun.

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

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

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

So this is the
associative property.

Which one of the
equations on the right

represents the commutative
property of addition?

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

in which we're
doing the operation.

So a plus b is
equal to b plus a.

Which one of the
equations on the right

represents the commutative
property of addition?

Well, that's what
they just asked us.

a plus b is equal to b plus a.

And we are done.