Let’s do some problems with

the distributive property. And the distributive property

just essentially reminds us that if we have, let’s say, a

times b plus c, and then we need to multiply a times this,

we have to multiply a times both of these numbers. So this is going to be equal to

a times b plus a times c. It will not be just a

times b then plus c. And that makes complete sense. Let me give you an example. If I had said 5 times 3 plus

7, now, if you were to work this out using order of

operations, you’d say, this is 5 times 10. So you’d say, this is 5 times

10, which is equal to 50. And we know that that’s

the right answer. Now, use the distributive

property, that tells us that this is going to be equal to 5

times 3, which is 15, plus 5 times 7, which is 35. And 15 plus 35 is

definitely 50. If you only multiplied the 5

times the 3, you’d have 15, and then plus the seven, you’d

get the wrong answer. You’re multiplying 5 times

these things, you have to multiply 5 times both

of these things. Because you’re multiplying

the sum of these guys. Anyway. Let’s just apply that to a

sampling of these problems. Let’s do A. So we have 1/2 times

x minus y minus 4. Well, we multiply 1/2

times both of these. So it’s going to be 1/2

x minus 1/2 y minus 4, and we’re done. Let’s do C. We have 6 plus x

minus 5 plus 7. Well, here there’s actually

no distributive property to even do. We can actually just remove

the parentheses. 6 plus this thing, that’s the

same thing as 6 plus x plus negative 5 plus 7. Or you could view this

as 6 plus– So this right here is 2, right? Negative 5 plus 7 is 2,

2 plus 6 is 8, so it becomes 8 plus x. All right. Not too bad. That was C. Let’s do E. We have 4 times m plus 7 minus

6 times 4 minus m. Let’s do the distributive

property. 4 times m is 4m plus

4 times 7 is 28. And then we could

do it two ways. Let’s do it this way first.

So we could have minus 6 times 4 is 24. 6 times negative

m is minus 6m. And notice, I could have just

said, times negative 6, and have a plus here, but I’m

doing it in two steps. I’m doing the 6 first, and then

I’ll do the negative 1. And so this is going to be

4m plus 28, and then you distribute the negative sign. You can view this as a negative

1 times all of this. So negative 1 times

24 is minus 24. Negative 1 times minus

6m is plus 6m. Now you add the m terms.

4m plus 6m is 10m. And then add the constant terms.

28 minus 24, that is equal to plus 4. Let’s go down here. Use the distributive property

to simplify the following fractions. So I’ll do every other

one again. So the first one is, a

is 8x plus 12 over 4. So the reason why they’re

saying the distributive property, you’re essentially

saying, let’s divide this whole thing by 4. And to divide the whole thing by

4, you have to divide each of the things by 4. You could even view this as,

this is the same thing as multiplying 1/4 times

8x plus 12. These two things

are equivalent. Here you’re dividing each

by 4, here you’re multiplying each by 4. If you did it this way, this is

the same thing as 8x over 4 plus 12 over 4. You’re kind of doing a adding

fractions problem in reverse. And then this 8 divided

by 4 is going to be, this’ll be 2x plus 3. That’s one way to do it. Or you could do it this way. 1/4 times 8x is 2x, plus

1/4 times 12 is 3. Either way, we got

the same answer. C. We have 11x plus 12 over 2. Just like here. We could say, this is the same

thing as 11– We could write it as 11 over 2x, if we like. Or 11x over 2, either way. Plus 12 over 2 plus 6. And let’s just do one more. E. This looks interesting. We have a negative out in front,

and then we have a 6z minus 2 over 3. So one way we can view this,

this is the same thing, this is equal to, negative 1/3

times 6z minus 2. These two things

are equivalent. Right? This is a negative 1/3. You could imagine a

1 right out here. Right? Negative 1/3 times 6z minus 2. And then you just do the

distributive property. Negative 1/3 times 6z is

going to be minus 2z. And then negative 1/3 times

negative 2, negatives cancel out, you get plus 2/3. And you are done.

## Comments

Author

Can you do some problems involving absolute value equations?

Author

Question: Where are you getting these problems?

Author

I had to watch this for math class…

Author

some of your videos i watch just to see how much of it i dont get

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:veryhappy:

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Thank you so much Khan

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Thankssss!!(:

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thank you i had to learn this in 10 seconds

Author

This is great video to Learn Maths .

Author

I have a feeling almost all of us had to watch this because of math/ algebra class

Author

THANKS

Author

Khan, my indian, mathematic hero!!!!

Author

I doubt that most people watch it for fun

Author

there is the 0.01%

Author

Better than my teacher -__-

Author

Sal, I don't know if you'll read this but this is where my voyage begins in mathematical exploration. I have taken algebra and statistics at my local community college and have decided that I would like to minor in mathematics. I started to teach myself calculous but found my math to be a little rusty so here I am. Let's see if I'll be a math wiz in 2 years like I'm hoping. Hey, it took Newton less time to invent calculous than most freshman take to learn it in college.

Author

6 divided by 3 becomes 2, now 1 over 3 is divided into 3 and becomes a unicorn, now take 12 and make that a bear and then remember it needs a orange in its butt so that becomes another 12…

Author

thanks so much, this really helps!

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there is a mistake

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Huh?

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thx

Author

Cooll

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We used this in Pre algebra class

Author

Better than class

Author

Thanks for helping me pass my test (:

Author

I'm doing an extra credit project in which I have to ask a question so my question is why were the parenthesis brought down on the 4(m+7)-6(4-m) example after being distributed already?

Author

best math teacher

Author

Given 1/2(5), is the answer one tenth: 1/(2(5)) or half of 5: (1/2)(5)?

Does the distributive property count as a parentheses operation, overriding the left to right rule of multiplicative order of operations?

Author

I promise you one day you will get a big donation from me. This coming from someone who HATED school and now can spend hours without break learning. I want to thank you and your team for making Khan Academy!

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Helped me out

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Good problems

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2:07 5 + 7 isn't 2 it's 12.

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I know ur reading this

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I have a question, why did you leave parentheses in problem e?