Introduction to the Distributive Property
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Introduction to the Distributive Property

>>Professor Perez: Hey! This is Professor Perez again. Today we’re going to look an
introduction to the distributive property. Of course, we’ve got to get Charlie out here. He better be ready! Hey, Charlie, you ready to go?>>Charlie: Ya…>>Professor Perez: All right, here we go. Right here. Introduction to the distributive property. So, what the distributive property
is, is what we’re going to do, is we’re going to distribute a number across an
addition or a subtraction using multiplication. Let me give you an example here. 2 times 5 plus 3. Notice the 5 plus 3 is in parenthesis. Before we get to the distributive property, what we could do is add the
two numbers in the parenthesis. You’ll see when we get to
the Order of Operations, that that is what we’re supposed to do first. Okay, that’s coming up soon. So watch. We take what’s in
the parenthesis, 5 plus 3. What’s 5 plus 3, Charlie?>>Charlie: 8.>>Professor Perez: 8. Don’t forget we have a 2. Now what’s the operation, Charlie? It’s 2 outside of a parenthesis. There is no operation written
down, so it’s assumed to be what?>>Charlie: Multiplication.>>Professor Perez: Multiplication. And so, 2 times 8 is what, Charlie?>>Charlie: 16.>>Professor Perez: 16, same as 8 times 2. Now, same problem, but now we’re going
to demonstrate the distributive property. Notice there’s a 2 outside the parenthesis that 2 outside the parenthesis
means you’ve got to multiply. But, you don’t have to add what’s in the
parenthesis first, you can add 5 plus 3, but what we’re going to do is
we’re going to distribute the 2 to the 5 and to the 3 by multiplication. Watch, Charlie. We first start with 2 times 5. So we’ll bring that down. We did 2 times 5. And now, in the parenthesis our operation
was addition, so we’ll bring that down and now we take the 2 and multiply
to the 3 and that’s 2 times 3. Notice the 2 was distributed to each the 5
and to the 3 and operation is multiplication. And now, what’s 2 times 5, Charlie?>>Charlie: 10.>>Professor Perez: 10, same as 5 times 2. And what’s 2 times 3?>>Charlie: 6.>>Professor Perez: 6, same as 3 times 2. And anyway, what’s 10 plus 6, Charlie?>>Charlie: 16.>>Professor Perez: 16 and notice
the two answers are exactly the same. 16. Now, of course, most of
you are probably saying, “Well, I’m just going to do the parenthesis first.” Yeah, but you can’t do that
all the time, you’ll see. Because I know you’re asking, “When am I
ever going to use the distributive property?” Well, you’ll see very soon. Now, same problem, Charlie. 2 times 5 plus 3. Now somebody mentioned this technique to
me so I’m going to go ahead and show it. 2 times 5 plus 3 basically means you have
two 5 plus 3’s a being added together, which is true, okay? And 5 plus 3 plus 5 plus 3, you
can add in any order you want. Remember adding numbers? You can add in any order you
want and we can just reorder it as 5 plus 5 plus 3 plus 3 which is 10 plus 6. Which is again, 16. Another way of looking at what’s 2 times 5
plus 3 in parenthesis, which is fine, okay? Now, here’s the example we haven’t
discussed variables yet in this class, but we’re going to demonstrate it right
now with this distributive property. Now, you cannot add x plus 3 in the parenthesis. Some people think that x plus 3 is 3x. No it’s not 3x. It is 3x if you want to repeat
this class, Charlie.>>Charlie: What? Huh?>>Professor Perez: Okay, x plus 3,
you cannot add those two together. 3x actually means 3 times
x, we’ll get to those later. But, x plus 3 you can’t add. So, are you stuck? No. You can apply the distributive property. You can distribute the 2
to both the x and to the 3. So, 2 times x is written 2x. 2x means 2 times x. And our
operation is addition in the parenthesis so we’ll bring that down. And we’ll take 2 times 3 which is what, Charlie?>>Charlie: 6.>>Professor Perez: 6, okay. You cannon add 2x plus 6
and that is your answer. So, you took 2 times the parenthesis x plus 3, and applied the distributive property
and then end up with 2x plus 6. So, we’ll be dealing with that a little
later in the semester and you’ll be dealing with that a lot in Beginning
Algebra which is the next class. Okay, now, let’s look at a
subtraction in the parenthesis, Charlie. Let’s do the parenthesis first. What’s 7 subtract 3?>>Charlie: 4.>>Professor Perez: 4 and you’re
multiplying by 2 which does give you 8 okay? Now let’s apply the distributive property. What do you, Charlie? Distribute 2 times 7 is…okay…and your
operation is subtraction so bring that down. And then what?>>Charlie: 2 times 3.>>Professor Perez: Okay,
2 times 3, that’s right. All right, now, we did 2
times 7 is what, Charlie?>>Charlie: 14.>>Professor Perez: Okay, bring
down your subtraction, 2 times 3 is?>>Charlie: 6.>>Professor Perez: 6, and what’s 14 subtract 6?>>Charlie: 8.>>Professor Perez: 8, same answer, okay. Now we’ll go to this next one. Here we’re going to distributive
across a subtraction and an addition. Same process. We take 2 times 7, bring down your
operation which is a subtraction, and then we have 2 times 3
which is…going to be 6. Bring down our addition and
then we have 2 times 2, right? Okay, so let’s do 2 times 7 is what, Charlie?>>Charlie: 14.>>Professor Perez: Subtract 2 times 3>>Charlie: 6.>>Professor Perez: Add 2 times 2.>>Charlie: 4.>>Professor Perez: Very nice, okay. Now remember, you’ve got to work left to right. 14 subtract 6 is what, Charlie?>>Charlie: 8?>>Professor Perez: 8. We’ve still got to add the 4 and what do we get?>>Charlie: 12.>>Professor Perez: Very
nice there, Charlie, yes. Now, the problem could have
been…uh…the answer could have been gotten by first doing the operations
in the parenthesis. 7 subtract 3 is 4, and 4 plus
2 is 6, and 2 times 6 is 12. Yes, that would be faster, but we’re trying to demonstrate the distributive
property, how it can be used. Okay, well, let’s do 2 times 43. Well, let’s think about how do we do this. Well, first, let’s break the
43 in the expanded form, okay? 2 times 40 plus 3 and if we distribute
the 2 through, what’s 2 times 40, Charlie?>>Charlie: 80.>>Professor Perez: 80. And we have an addition, and 2 times 3 is?>>Charlie: 6.>>Professor Perez: 6 and that gives you 86. So this is another way of looking at 2 times 43. Well, a lot of us tend to want
to use this vertical format. What you are soon going to see is this
vertical format, the reason it works, is because you’re using the
distributive property. It’s exactly what you’re doing, watch. 43 times 2. The first thing you are taught
to do is do what, Charlie?>>Charlie: 2 times 3.>>Professor Perez: 2 times 3 which is 6, yes. See? It’s the distributive property. 2 multiplied by 3. And then you take the what?>>Charlie: 2 times 4.>>Professor Perez: Go diagonally and go 2
times 4, which is 8 and you bring it down. Notice you put the 8 in the tens
place because you have 8 tens, which is actually 80 and
so 86 is just 80 plus 6. That’s your vertical format. Watch, let’s do a more complicated one. Let’s do 6 times 134. Don’t get scared! What we’re going to do is
write 134 in expanded form. In expanded form Charlie, what’s 134?>>Charlie: 100 plus…>>Professor Perez: That’s right. 100 plus 30 plus 4, okay, now,
apply the distributive property. What do we get, Charlie? What do we do first?>>Charlie: 6 times 100.>>Professor Perez: 6 times 100 is 600. Bring down our operation. What’s next?>>Charlie: 6 times 30.>>Professor Perez: 6 times
30 which is what, Charlie?>>Charlie: 180.>>Professor Perez: 180, because 6
times 3 is 18 and 6 times 30 is 180. Okay, Charlie, 6 times 4 is what?>>Charlie: 24.>>Professor Perez: 24, okay. So we work left to right, 600 plus
180 is 780 plus 24 which is 804. that is the answer. Now, Let’s do the vertical format. Now, we’re going to a vertical
format without carrying over. You’ll see what I mean. Watch, we first start with 6
times 4 which is what, Charlie?>>Charlie: 24.>>Professor Perez: 24, that’s
the distributive property. And then we do 6 times 3 which is 18. Now notice, the 3 was in the tens place, so
the 18, the 8 is written in the tens place and we bring down a place holder, 180. And then we go 6 times 1 which is 6. It’s in the hundreds place, we have 6
hundreds and we put in our place holders there and you add them all together and
the first column is what, Charlie?>>Charlie: 4.>>Professor Perez: 4. Okay, and then we have the 2 and 8 is 10. Put your 0, carry your 1,
and 1 plus 1 plus 6 is 8. It’s 804. That’s without the carry over. Well, let’s finish this lecture
by doing the carry over here. Okay, here we go Charlie, pay attention. 6 times 4 is 24. Put the 4, carry the 2. 6 times 3 is 18, right? Add the 2, is 20, put your 0 down, carry
the 2, and 6 times 1 is 6 plus 2 is 804. So there you go. That’s the vertical format. But these vertical formats are using the
distributive property, so there you go. That’s your introduction to
the distributive property. So, we’re going to work on
multiplication more, in the future, anyway, keep up with your homework and
we’ll see you all again soon.


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