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The distributive property

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Distributive property example 1

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Distributive property example 1

Discussion and questions for this video
What is Sal referring to as "x" and "y"? can anyone explain or link to a video
He uses "x" and "y" since they represent an unknown value.
1 Comment
do I use the distributive property for the problem (7)(m+3) to get 7m + 21 or because there's parenthesis around the 7 is it 7 x m + 3
The parentheses around the 7 don't matter. So, you can basically just do the distributive property.
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When you did problem c. 6+(x-5)+7. Why didn't you perform distributive property?
1 Comment
There is no distribution taking place in this problem because everything is addition; no multiplication at all. Or if you'd like to think about it this way, there is a 1 hiding in front of the left parenthese, so distribute the 1 and you get 6 + x - 5 + 7.
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whats with the m c x y stuff i dont get it
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m c y x are all variables used in math, but they are most commonly used in algebra.
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i didnt understand his example: E. 2:31
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hmmmm....I don't know if I can explain it better, but I'll try...ok the problem is 4(m+7)-6(4-m). Now to distribute you start by simplifying...4(m+7) is the same as 4 x m +7...but the distributive property lets you multiply both of them, like so...4m + 28. Now your problem looks like this...4m + 28 - 6(4-m)... Now you do the same thing here as you did with the first. So now your problem looks like this... 4m + 28 - 24 + 6m...Next you combine like terms...6m + 4m = 10m...28-24 = 4...So your answer is 10m + 4

Hope that helps!
1 Comment
when your doing e, why do you put parenthesis around 24-6m but you don't put it for 4m+28 ?
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because he didn't distribute the -1 into the quantity, Just the +6.
Could have just said -24+6m without parenthesis.
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At 1:50 it looks like the problem is 6(x (MINUS) 5)+7, but Sal turns it into 6(x (NEGATIVE) 5)+7. Can someone please explain why this happens/happened?
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but if it is a minus, won't it become
6 + x - 12 ?
if it is a negative it becomes
6 + x. 2
I am confuse on this part too
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in question c) .. 11/2 we don't divide them ?
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well you can't divide evenly. =)
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Why is math so boring? I'm learning about distributive property and algebra. WHEN AM I GONNA USE THAT IN LIFE? Why can't I learn about taxes huh? From what I've heard that is pretty hard. What about bills and buying houses? Do they teach that in school? NO. I would really appreciate if you would put up a video about that. Please and Thank you. x
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I wanted to know the same thing in school. So maybe this will help (maybe not we'll see)
Lets say you want to know why you trip the circuit breaker when you turn on your electric heater? it helps to know that;P=E*I
P (watts) = E (electromotive force) * I (Amperage)

That is algebra in the real world. Maybe you won't be an electrician but be glad the electrician knows algebra :)
1 Vote
I am 'struggling' on the Rational Number Word Problems test and this question has me completely confused. I don't understand the part where it says we simplify d - 0.035 * d to d(1-1.035) using the distributive property. How do we just drop a 'd' and earn a '1'? I pasted the whole word problem with the first few hints below.

The earth's orbit around the sun is not a perfect circle. Let's call the smallest distance from the earth to the sun d. Earth's farthest point from the sun is equal to 1.035⋅d. If the distance from the earth to the moon is currently 0.0016⋅d, how many times larger is the distance between earth's farthest and closest point than earth's distance to the moon? (Express your answer as a simple fraction in lowest terms)

We first need to find the distance between earth's closest point to the sun, d, and earth's farthest point from the sun, 1.035⋅d. How do we find this?
To find the distance between d and 1.035⋅d, we need to compute the absolute value of their difference. What is |d−1.035⋅d| equal to?
Using the distributive property, we see that the difference d−1.035⋅d is equal to d⋅(1−1.035). Since 1−1.035=−0.035, this is simply equal to −0.035⋅d. What is the absolute value of −0.035⋅d, and how do we use it to get the answer?
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I'm going to assume that you do know the distributive property. So when we have d(1-1.035) and we distribute to both of the terms, we end up with d - 1.035d.
What is unique about the distributive property though, is that it works in both directions. Essentially since we know that d(1-1.035) = d - 1.035d, we also know that it works in the other direction, so d - 1.035d = d(1-1.035). What really happened is, we divided each term by d so that the d was on the outside of the parentheses. d/d = 1. and -1.035d/d = -1.035. Putting these all together gets d(1-1.035). I hope I answered your question. If not, I apologize.
1 Comment
where did you get the -1? at exercise e).
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Because when you have (Example) -(4x-5) is the same as (-1)(4x-5), so in the question that Sal does its: -(24-6m) is the same as -1(24-6m) or (-1)(24-6m). This causes you to change all the signs within the brackets.
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i am a 5th grader going into 6th next year, and i was wondering if someone can answer this question:
do you think i am old enough to be practicing distributive property, because i have to do this unit on mult. and div. and i am wondering if this is expected of me. i do not know how to work with negative numbers, which makes this all even more confusin than it already is.
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I think you're at a good age to learn the distributive property. But, you will have to know how to work with negative numbers, so you should learn that before you go on to the distributive property. Hope I helped :)
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What does all that a b and c mean? I know that they are variables, but does he have to use them? Please help!
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He doesn't have to. But it's a good idea to get comfortable to seeing different letters other than "X" and "Y" used as variables. In science classes, you'll need to use different letters to keep track of everything.

Here are some common letters that are used as variables:
t, for time
d, for distance
v, for velocity (velocity is like speed, but you have to pay attention to where you're going)
a, for acceleration (how fast you're speeding up)
1 Comment
How do you remember the differences between commutative, associative and distributive law of addition ? That is, without mixing them all up!!
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I remember them by thinking of the roots of the words and what the words mean to me.
Commute: means to go back and forth (like in a car) doesn't change the equation if you move a + b or b + a
Associates: are the people you hang out with, you can add or multiply them any order you want, they are still your friends (a x b) + c or a x b + c
Distribute: I think of like giving out snacks (distributing) if I give one to one friend I have to give one to every friend a(b) x c or a x b + a x c =
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At 1:34, example c, why is it possible to just remove the parentheses and go on like there haven't been ones? Aren't they here for a reason? To calculate x-5 first, meaning before 5-7? I don't understand!
1 Comment
There's not necessarily a reason; sometimes they just put parentheses to trip you up in exams, to see if you know your operation rules. One of those rules is: addition is commutative. It doesn't matter if you do 3 + 5 + 6 or 5 + 3 + 6, you'll get the same result.

Subtraction is the same as adding a negative number, so it's commutative too. Hence you don't need the parentheses in 6 + (x - 5) + 7, and can do the operation in the order you want, as long as you make sure the negative sign stays with the 5. What I mean is, you can't go "OK, let's do 6 + 5 + x - 7". But other than that, you can do what you want!

Lastly, as I said, subtraction is commutative, which means you can change the order of the terms and it won't change the result. But you might say "that's not true, 6 - 8 isn't the same as 8 - 6". To which I'd reply: no, they aren't the same BECAUSE you put the negative sign on another number. As I said above, subtraction is like adding a negative number; that means that 6 - 8 is really 6 + -8. You can change the order, but no matter what you do, 8 will have to stay negative. You can't just make 6 negative instead, that's not part of the commutative law! So the only way to rewrite 6 - 8 is -8 + 6.

Hope it helps!
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How would you be able to solve problems like 4(8n+2) ? Or at least point me to the section where I can find videos to solve distributive property equations like this one. Please >_<
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To solve this just think of what it is telling you to do by how it is written. In words, it would be: multiply everything inside the parentheses by 4.
So, 4 x 8n = 32n and 4 x 2 = 8. Now that you have the distribution done you have the answer:
32n + 8
Hope that helps.
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I don't understand the importance of the distributive property. Could someone explain it to me? Also, what kind of career uses the distributive property?
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The distributive property, when manipulated to its fullest, can be extremely useful. Once you get into Algebra, you will learn FOIL, which is an extension of the distributive property that lets you multiply (a+b) times (c+d) to a(c+d)+b(c+d) to ac+ad+bc+bd. Once you do that, you can do the opposite and bring ac+ad+bc+bd back to (a+b)(c+d). This will help you solve equations with x^2 in them [you will factor from x^2+(a+b)x+ab into (x+a)(x+b) instead of (a+b)(c+d)], which can help you find where thrown objects will land on the ground by approximating their path using functions with x^2 in them.

However, that's much for a much later time. The uses of this simple distributive property are more daily-life than the above example given. For example, if you know that the number of bottles you must distribute to 3 children and the number of bottles you must distribute to 7 children is 40 and the number of bottles per student is the same, you can set up the equation 3a+7a=40. With the distributive property, you know 3a+7a=a(3+7)=10a, so 10a=40, or a=4. Adding like terms (adding terms with the same variables) is used many times in math and you'll find it helpful in careers.

I hope this helps!
1:14 what does sampling mean?
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Definition: a small part or quantity intended to show what the whole is like.
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Whats the difference between associative, communitive and distributive.
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Commutative-The order of the numbers in multiplication or addition doesn't matter.
Examples:
1+2=2+1
27*8=8*27

Associative-The placement of parentheses doesn't matter if there is a close parentheses for every open parentheses and the operations are either all addition or all multiplication.
Examples:
(27+38)+9=27+(38+9)
(6*5)**4=6**(5*4)

Distributive-A number multiplied by two or more addends together is that number multiplied by each addend separately.
Examples:
3*(47+37+3)=3*47+3*37+3*3
4*(2-1+3)=4*(2+(-1)+3)=4*2+4*-1+4*3=4*2-4*1+4*3
6*(56-34)=6*56-6*34

The commutative property has to do with moving numbers around in addition and multiplication, the associative property has to do with moving parentheses around in all addition and all multiplication, and the distributive property has to do with distributing a multiplied number to many addends.

I hope this helps!
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Two negatives become a positive abd you keep the variable.
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I think it is true
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is ) I* IO \$ @ ()*&(87978(*7(78(*79*&9 can they all be variables?
All those can be variables.
A variable can be any number or symbol.
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How do you solve this?
-5(y+5)=15y
This is what I did
-5 times y equals -5y+ -25=15y
but then do i add or subtract the 25 to both sides?
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1) First distribute: -5 (y+5) = 15y -> -5y - 25 = 15y.
2) Then get y by itself by subtracting -5y (or adding 5y) from both sides:
-25 = 20y.
3) Then divide both sides by 20. -25/20 = 20y/20 -> y = -5/4.
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I don't under stand what the fancy x means. Can anyone help me?
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I think he is just using it as a variable, to express an unknown, or part of a mathematical property.
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Is there a way to flag a video for future viewing? I am thinking that this will become more relevant as I progress further. I was lost with fractions and other operations.
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Sharon, you are correct. Distribution is something you will use constantly as you progress into more complex math problems. Actually, it's a very easy concept and you'll have a lot of fun with it! I would suggest that if you have had problems with other things like fractions, go to your exercise dashboard and do drills over and over and over. Just like anything else, practice makes perfect. Or close to it. I've found if I run up against something that stumps me, it means I haven't perfected my understanding of something that came before. Keep me posted!
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Why do you sometimes change the addition or subtraction to its opposite?
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is sunlight matter
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Yes, sunlight is matter because anything and everything that takes up space is matter. Good job on figuring that out!

Except some people say that sunlight doesn't take up space and some people say it does, so it may or may not be matter...
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Give a thumbs up SALS AWESOME. He helps with everything. Anyway, isn't a variable only X and not Y or M.

Thanks
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Thank You SALS STILL AWESOME
1 Vote
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Did anybody see the opening ceremony for the london 2012 olympics.
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for the problem 11x+12/2 would the answer still be right if I put 5 1/2x+6?
1 Comment
Given:
11x + 12/2
Division property of equality:
11x + 6

The answer to your problem is 11x + 6 not 5 1/2x + 6
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wht is six -x
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6x simply means 6 times a number that we don't know. We represent that number we don't know with a _variable_. A variable is a letter or symbol to represent a *number*.
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At 4:40, why did he skip over b?
Sal says "I'll do every other one again." He did it on purpose, to do less of them and/or save space and/or something else.
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Why do people say over instead of divide?
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Mostly because there is no difference from division and a fraction. There is no difference from putting 1 over 2 or 1 divided by 2. Fractions are division problems, and vice versa.

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i'm not getting the m and the x thing
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In mathematics letters [like m and x] are often used to represent numbers we either to not know what they are [yet] or do not care what they are [because it does not matter]
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what does x and y and m and all that mean?
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When we have numbers that can be very different depending on the situation, (for example: Let's say that for every kid in class you need 3 pencils and 2 pens and 1 eraser, and you have to write a 'rule' into the computer program- you know, how many different stuff it should order for every class,)- we just call the numbers names, usually letters like x y or z, and the computer can add them up for every class separately!
If you get this video, it's just a matter of time and practice before you are acing calculus!!!
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At 0:49, why do we have to multiply first then ad? Wouldn't it be much easier to just ad then multiply?
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Because of Order of Operations! (:
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Why did they create this rule!
:-(
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To make many problems that this rule can apply to easier to solve
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Simplify the following expression:

−2(9m+1)+7(−9−5m)

Distribute the −2 into the first set of parentheses:

−2(9m+1)+7(−9−5m)

−18m−2+7(−9−5m)

Distribute the 7 into the parentheses:

−18m−2+7(−9−5m)

−18m−2−63−35m

Rewrite the expression to group the m terms and numeric terms:

−18m−35m−2−63

Combine the m terms:

−53m−2−63

Combine the numeric terms:

−53m−65

The simplified expression is −53m−65.
This problem was in the practice section of the website.
I am confused about how the negative(subtraction), addition signs work. The answer I came up with was -53m+-65 and it told me I was wrong. Is that correct? The only problem I am having is with the addition subtraction(negative) signs. Please give an detailed answer.
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what does x,m,z,and y mean?
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They are variables. They represent numbers of unknown value.
What do the letters mean? I don't understand that.
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they are variables .In this they are the unknown numbers
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first part question c? i did not get that at all
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Can you be more specific? This problem didn't have any distribution to be done, so all Sal did was remove the parenthesis and evaluate the expression normally.
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I don't understand where the negative 1 (-1) came from in the "e" question. Can somebody explain me?

I'm talking about the expression 4(m+7)-6(4-m)
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With the expression - (24 - 6m), you have to distribute the minus sign to all parts in the parentheses. A good way to think of it is that there is really a 1 after the minus sign (which is true). So it can be rewritten as -1(24 - 6m). You don't need to put the 1 there, but if it helps you, then put it.
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I still don't get the difference between x and y
1 Comment
x = Independent Variable
y = Dependent Variable
The value of y depends on the value of x.
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do I use the distributive property for the problem (7)(m+3) to get 7m + 21 or because there's parenthesis around the 7 is it 7 x m + 3
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You had it right the first time. Since the parentheses go around the 3 as well, it also gets multiplied by the 7.

(7)(m+3) = 7m+21
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Why do they have to use letters instead of numbers? its very confusing
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the letters represent numbers that we don't know yet.
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so you put sand b together (ab) so thats multiplication right?Couldn't you just put a multiplication sign or a dot?
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Because using variables, x being one of the most popular, will make people confused if you have something multiplied with x, for example, ax instead of axx. The dot is up to preference.
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At 4:41 , Sal said that you divide 11x/3. What do you do if the division isn't even?
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You have a decimal on 4:41
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When will koalas finally conquer the world
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Does this have anything to do with math??/
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A negative multiplied by a negative is always a positive.
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Yes, you are correct. :)
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what is 6* (a+7) is it 48a or just 6a+42
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Using the distributive property: 6 * (a+7) becomes 6 * a + 6 * 7, therefore it becomes 6a + 42.
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These are my school math school problems:
1st 4(9m+6b+4)+r
2nd: 8tr+10t+14t squared +13
3rd: 3m +2t-10r-7
4th 4y+2x(5y+12)+y squared
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To reduce the problems.
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at 2:24 what does M mean ?
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'm' is just another letter used for the unknown number. It is the same thing as using x. some people prefer to use x, y, and z or a, b, and c(the most common letters).
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im confused what are the m + 28 and all that stuff i do not get any thing he is syaing :(
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how do you solve if one or more variables are unknown
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You do basically the exact same thing.

EXAMPLE: 3(x + 4)
First, you would need to distribute the 3.
3x + 12
This is as far as you can possibly simplify this expression, as 3x and 12 aren't like terms.

EXAMPLE: here is another example.
x(5+2)
First, distribute the x.
5x + 2x
You can simplify this further, as they are like terms. You get:
7x

I hope hope this helps!
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I always struggle with distributive property. It seems like I always get different results when I attempt new problems I have never seen. Is there an 'order' to distributing - like order of operations?
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I didn't understand what Sal did.Can someone help me?
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can any body else help me
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does anyone else have 45 meteorite badges????
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Not me I have 141 meteorite badges.
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nice
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y wont my video work
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It's possible that you need to install or update Flash or Java. Go check their websites to see if you have the latest updates, if you don't know how to do that ask someone you know to help you.

*edited for clarity
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For Question C how come the five stays the same and isn't multiplied? Is it because of the plus sign?
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Why did you divide the 8x by 4? aren't you supposed to leave it as a fraction since their not the same?
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id like to have some help
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what does a and b and c and d and e and f mean?
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Variables.Variables are numbers repesented by numbers
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were did you get the 50?I do not under stand.
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The original problem looks like this: 5( 3 + 7)
What is 3+7? 10, right? So, replace 3+7 with 10.
Now the problem looks like this: 5(10)
What is 5 x 10? 50, right?
So the question 5( 3 + 7) changes to 5(10)
And 5(10) is the same as 5 x 10, which is 50
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where did you get the -1? at exercise e).
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thanks for the help =)
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I really don't understand negative numbers. Its so confusing!!!!
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In example [E] Why do we have to put a 1 there? Is it required?
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i mean haw do that work because i don"t got it
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At 4:20

How did Sal turn (8x+12)/4 into 1/4(8x+12) - what are the rules behind this?
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At 1:51, why is the 5 negative? How do you know a minus symbol from a "negative" symbol?
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I don't understand wht you are talking about
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I find the distributive property contradictory to the next topic "Order of operations"? There we are thought to start with parenthesis but in distributive "property" we do multiplication first. Why? What is the difference?
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The distributive property can be used instead of the typical order of operations. It will give you the same answer either way. In algebra, when you need to solve for variables inside parenthesis, you can use the distributive property to solve a problem that would be impossible otherwise.
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what kind of property is 4x-2=2x+5 or how do you do it?
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dont worry i dont know too spellthem either i has terible gramr
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what is distributive property of rational numbers
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this video was very interesting. but, i was kinda confused at the end.
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If there is a variable in the equation, do you have to get rid of the number without the variable first?
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lets say there is an equation
7(x+4) = 12
there are two ways to solve
1. distribute the 7
7x + 28 = 12
then solve for x
x = -16/7 (pretty ugly, I just made up the problem)
2. divide by 7 first
(x + 4) = 12/7
then solve for x
x = 12/7 - 4
which is
12/7 - 28/7
which equals - 16/7
Hurray
hope this helped =)
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1 Comment
This is the very big problem with Khan Academy, you're working your way through Multiplication and Division, and suddenly algebraic variables and fractions are in very next video, before they're even explained.
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There is a video in the Algebra section called "What is a variable?
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What it there are two numbers in front of the parentheses such as
-a -b(x-y) c
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Only use the value directly before the parentheses, and since parentheses come first by the order of operations you cannot combine multiple values before the parentheses and distribute that. In your example, it would be -a - b(x) - b(y); the c doesn't have a sign before it, so I left it out. Or you could take the original expression as meaning -a + -b(x-y) in which case distributed it would be -a + -b(x) + -b(y) or -a + -b(x) - b(y), but as you can see it simplifies to be exactly the same.
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You go too fast. In example (a) how does 1/4(8x+12) equal 2x+3???
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Because in 1/4(8x+12) you are multiplying 8x and 12 by 1/4 (which is to say, dividing them by 4)
So, if you have eight X's and you need to split them into four groups, each one gets two X's
(they're using X as a variable, which means it's an unknown part of the equation, however I explained it literally as eight X's which works in this case)
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Is 1/2 x - 1/2 y - 4 the same as x/2 - y/2 - 4?
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Thanks I was really confused about that!!!
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Can someone do question (d) please. I don't understand what I should do if just a minus sign is behind the parenthesis.
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All parentheses have an invisible 1 in front of them, if no other number. The minus sign ( - ) means that there is a negative 1 in front. Distributing, make all the numbers inside the parentheses have the opposite sign of what they used to.
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Ok, for expression (b) 0.6(0.2x + 0.7) that would end up being 0.6(0.2x) + 0.6(0.7) = 0.12x + 0.42. Is that (a) the right place to stop and (b) the right answer?
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A) Yes and B)yes. :)
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How does -1 times -6m become +6m I do not understand
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ok so we're just supposed to know it that's like asking a toddler to do multiplication
why not give us more videos in our language because I don't know about you but I don't speak collage but I sort of understand collage vocab words my brother is in collage
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Alright, I'm going to try to explain this. Lets say you have a distributive property question in front of you. It looks like this. 12*(3+4) is equal to, greater than or less than 12*3 + 12*4. So, before your brain explodes in your head, just remember that this can be solved using basic + and *. The first part says 12 times(3+4), which is 12 times 7, or 84. Now your question says 84 (< , < ,=) 12*3 + 12*4. Now, we simplify the second side. 12 times 3 + 12 times 4. First, 12*3 =36 and 12*4 =48. Now your question says 84(< , > ,=) 36 + 48. Now you just add 36+48, which equals, oh look! 84! This will always work because of the distributive property. If you would like to try this, the model for the distributive property is A*(B+C) = A*B + A*C. Hope this helped! If you go into community questions I answered another question just like this, so if you don't get this version, look at that other one
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So in question a) 8x+12 over 4
we divide 8 by 4 and 12 by 4 but why not x by 4?
I thought x represented a number as well.
Is this explained in another video?
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8x is one term, and 12 is one term, and when you divide a term by something you divide only one of the numbers.
example 12(12) over 3. You can divide just one of the 12s by 3 and get 48 (what you get when you do 144 divided by 3.)
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I don't understand this video all together. Can someone help me?
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Well I din't get the concept right like (a+b) can you try to make it more simple for me?please.............? I have not learnt sqaures.so it's hard to understand
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(a+b) stand for different numbers. a is one number, and b is another number. So in the video Sal has: a(b+c). Now remember that all the letters (a, b, and c) stand for a number. Using the distributive property we multiply a x b and then add a x c to that. So in the end we get ab + ac as an answer.
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ok when i was doing combining like terms with disstribution i had a lot of trouble carrying the variables, like the n's and x's and v's.... is there another way to like do it and still remember to carry the variable?
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So if I were to ask what's dis. proprty what would you say????
It is hard and how do you dod it !?!?!?!
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The distributive property is used to distribute a term on the outside of the parentheses to each term on the inside of the parentheses, and you distribute by multiplying.

For example:
3(x + 2)
= 3(x) + 3(2) {used distributive property to distribute the 3}
= 3x + 6 {multiplied 3 by x and 3 by 2}
http://www.algebrahouse.com
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Can you combine this property with the commutative property?

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What do you mean 'combine'?
I don't think so.
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how did he know all the stuff with out paper
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He does the math by writing on the board so you can see how to do it.
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Why is distributive property hard
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this is difficult for some one my age can some boy help me please?
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Haha, then why are you doing it? Basically, you just need to take the number in front of the parentheses and multiply it by everything in the parentheses.

Ex) 2(1/2x+54) would equal 1x+108
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In example (a) 1/4(8x+12) how does it equal 2x+3??? You explain too quickly, I think :/
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Using the distributive property you need to take whatever is outside the parentheses, in this case (1/4) and multiple it to each element in the parentheses. So in this case it would be like this.

1/4(8x+12) original equation then you apply the distributive property
(1/4)*8x + (1/4)*12 then you simply to
2x+3 because you are multiplying each constant by (1/4)
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For letter E we used a 1 while completing the equation, please explain why? i did not see that it was used or an explanation as to why it was used in previous lessons
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i do not get how you do it with fractions
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At 4:35, could the improper fraction 11/2x be converted into 5 1/2x + 6?
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What about questions like 2(36) for distributive property?
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For c) the 5 was not negative, so instead of 8 + x the answer would be 18 + x right?
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No, you would have to change the addition sign to a subtraction sign and then do the math.
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5(4x-3)+8= -2

show me how this is done
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Report a mistake in the video
Example:

At 2:33, Sal said "single bonds" but meant "covalent bonds."

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