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.