we use the same rules from multiplying in algebra that we do in basic math
say you're going to need to know them
let's take a look at them
there are basically five properties of multiplication
and you'll need to know them
there's the multiplication property of zero
the multiplication property of one
the commutative
property of multiplication
the associated property of multiplication
and i told you there were five, the distributive property
and really the distributive property is called the distributive property of
multiplication over addition it uses both
let's take a look at each
the first one the multiplication property of zero, i bet you already know
but we'll need to use this in algebra
in plain language the multiplication property of zero is
anything time zero
is gone anything time zero equals zero
very simple isn't it
so five times zero
is zero
even x time zero, I said anything times zero
equals zero
anything (indistinguishable word)
times zero
equals zero ok so that's a that's a first that that was an easy one
what about the second property
the second property of multiplication is the property of one
we talk about multiplying by one
now anything times one
is going to equal itself
so five times one of course
equals five
x times one, don't let it scare you,
is going to equal x
even (indistinguishable word)
times one
equals (indistinguishable word)
I don't even know what it is but if i multiply it by one
I get
itself
okay that's two down
what about the commutative property of multiplication, we'll use this in the future
as well
that is
you're allowed to switch hence the word commute
you're allowed to switch the order
of the things getting multiplied, the factors, when you multiply
so five times seven is the same
((SFX)) as seven times five note we switch them didn't we
hmmm, this has three things. two times ten times three order doesn't count is the
same as ten times two times three note I switched
the ten and the two
okay
you don't have to switch everybody as long as you switch anything the reason is to switch the
order
is commutative property
see that we flip those
and note that this switching doesn't work for all the operation it works for
addition and it works for multiplication
it doesn't work for subtraction and division
for instance
seven minus five
is not the same as five minus seven
seven minus five is two, five minus seven
is not two, its negative two
okay
don't need to worry about that right now all we need to know is that you can't switch
it
and ten divided by five
is not
the same as five divided by ten
so we can't flip negative, uh uh we can't flip subtraction and division but we can
commute
multiplication and addition
the next property is often confused with the commutative property
the associative property of multiplication
because the order of something changes it's just not the order of the
terms
when you're multiplying more than two things of three or four usually three
you are allowed to do them in any order
now see you're allowed to multiply them in any order
doesn't matter which two you associate first now note this
problem here two times ten times three
we're going to say that that's the same
obviously as two times ten times three
alright note that the order did not change here two
ten and three is still in the same order, two ten and three but the
parentheses are telling me to actually execute a different part of the problem first
on the left side
i multiply the two and the ten
first
i'm associating a different thing now two and the ten
and getting twenty
on the right side
I'll associate the ten and the three
but look at both sides twenty times three
sixty will be the same as two times thirty sixty
so it really didn't matter which two I did first
and note i didn't change the order
of the terms it's still two ten and three
two ten three on both sides it's the order that i executed the multiplication
now like other operations
or like other properties this doesn't work
for subtraction and division it only works for addition and multiplication
for instance here
if i change the order
i'm going to get different answers
as you can see
if i do that on the left side the ten minus seven first
I'll get a three minus two, I'll get one
but on the right side
if i do the seven minus two first i get five and that's a completely different answer
ten minus five
that's five
okay ((SFX- way off, I say you're way off this time))
so this associative property
uh... only works
for multiplication and addition not for subtraction and also not for
division ((SFX))
let's see if you can tell the difference between two things
to statements that have a commutative and have the associative property
in this statement, why is this statement true?
well let's see look on the right side and what changed it started off as
seven times three times five
and it became on the right side three times seven times five what changed
was that
the three and the seven
changed order, who tells me i can commute
the three and the seven
it's the commutative property okay
lets do another
now this one has parentheses, this is a tricky one
let's look at two
times four times five
and on the other side two times four times five
oh now i'm sorry two times five times four
the parentheses did not change did they?
the parentheses did not change
when the parentheses changes it's associative but they didn't change ((SFX))
what changed was the five and the four, I tricked ya.
this one again, is a commutative property
this one
the parentheses changed, didn't they? but the order did not
this is two four and five
on the left side and to four and five on the right side, the only thing that
changed was the parentheses ((SFX))
see how the order stayed the same but the parentheses changed
that's the associative property
you see why people get confused
so when the order of the factors changes
it's the commutative property
((SFX)) and when the parentheses change
it's the associative property, got it?
now we have one
last property that you'll need to know and it's probably the most important of
all
that's the distributive property also known as a distributive property of multiplication
over addition
basically what it says is ((SFX - well isn't that special))
it is the one
special exception to the order of operations
what the exception is that in this situation and i'll show you this one
situation
you don't have to do what's in parentheses first
you could do what's in parentheses first but you don't have to
see where we could and the three and the four first
but were also allowed to distribute the two
to each of those, the two is multiplying
and the three and the four are adding hence you see that multiplication over
addition
so we're going to distribute the two
to the three
and also
to the four
and then do it two times three plus two times four
that's another way to compute this
and this one instead of adding the five and six we could
distribute the ten to the five
and that to
distributing the ten to the six
you've got to say to yourself why would i do this why would i ever do this
well
there is going to be a time when you can't
do what's in parentheses first
for instance in this situation
we can't
do x plus five, I don't know what x plus five is they're unlike terms
but the distributive property allows me to distribute that ten
to the x
and get an answer
and distribute it to the five
and get an answer
and that's what they expect you to do when they say distribute
ok, it's going to allow me to do a little bit more
but it is make no mistake an exception to the order of operations which you
should have memorized by now
we're going to be using multiplications so let's make sure that you know how to
do somewhat some long multiplication
let's take that two
and i'm only going to do
two numbers at a time, gonna multiply it by two times nine
first and then I'm gonna look at the eight
and what will I get?
again eighteen hockey that my hand i can only write one numeral down there
so i'm going to write
the eight
what do I do with the one? well, the one really isn't the one it's a ten
because it's in the ten spot
so i'm going to carry it
carry it over to the ten spot and remember where was
I'm still going to multiply two times eight
its sixteen and what do I do with the one
add it to the result
and now i'll write that
seventeen
and that's my answer
this we call partial products multiplication
fancy word, remember products is the answer to a multiplication problem
all that is saying is that we're gonna do part of the problem at a time
okay i'm going to do the two first
then we're going to do the five, watch
let's do the two first
we just did one very much like that
two times nine
is what, eighteen, and I write the eight
carry the...carry the one
now two times eight
not done with the two yet
is what
sixteen
what do i do with the one?
add the one
get seventeen and then i'll write the seventeen
now i'm done with the two
whose turn is it
((SFX))
that's the fives turn, now that's really a fifty isn't it?
so i'm not going to start
writing my answer under the eight
because it's a fifty i'm gonna start writing my answer under the seven
five times nine
is forty-five
let's put the five
under the seven, like i say that's where we're starting
because that five really is a ten
it really is a fifty
that was forty five and I'm going to carry
the four from the forty five up here
and now i've gotta go five times eight
I get forty
what do I do with the four? Just like before add him to the result
and i'll write the forty four
now I have two parts of the answer
partial
products
let's add them together
eight and nothing is eight
seven and five is twelve so i write the two
carry the one
one one and four
is six
and then four and nothing
is four and there's your answer
not so bad because we do a little bit of it at a time
okay now I'll expect you to show that work
on the tests
obviously you can check it with the calculator but i want to make sure that
you show that work so you have to show your
partial
products
like the hundred and seventy eight the four forty five that you see there
if you don't show it, no work
no credit
let's get to it do the homework