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Distributive property algebraic expressions

Here we have some algebraic expressions to which we need to apply the distributive property. Now we're beginning to see how useful this property can be!
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Distributive property algebraic expressions

Discussion and questions for this video
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.
When you did problem c. 6+(x-5)+7. Why didn't you perform distributive property?
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.
in question c) .. 11/2 we don't divide them ?
You could, and get 5 1/2 (5.5), but sometimes its better to just have an improper fraction.
whats with the m c x y stuff i dont get it
m c y x are all variables used in math, but they are most commonly used in algebra.
What does all that a b and c mean? I know that they are variables, but does he have to use them? Please help!
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)
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?
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.
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
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 :)
where did you get the -1? at exercise e).
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.
when your doing e, why do you put parenthesis around 24-6m but you don't put it for 4m+28 ?
because he didn't distribute the -1 into the quantity, Just the +6.
Could have just said -24+6m without parenthesis.
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?
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
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.
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 :)
How do you remember the differences between commutative, associative and distributive law of addition ? That is, without mixing them all up!!
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 =
i didnt understand his example: E. 2:31
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!
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!
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!
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 >_<
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.
1:14 what does sampling mean?
Definition: a small part or quantity intended to show what the whole is like.
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?
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!
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.
could someone tell me why, when I do -5 x -11 it comes out -16?
-5x - 11 is as far as it goes. -5x - 11 is NOT equal to -5 -11 (that would be equal to -16 btw).

5x is a term and - 11 is an integer. Apples and oranges. There is nothing further to simplify.
why @ 4:37 is 11/2x and not 5.5x he divides the 12. why not the 11?
You could write 5.5x + 6 and it would be equivalent to what he does. However, in algebra the convention is to simplify a fraction and leave it at that instead of using decimals. 12/2 simplified becomes 6/1 which is written as 6. Also a convention.
Some teachers will mark you down when you turn a fraction into a decimal when the problem states to simplify the fraction.
Whats the difference between associative, communitive and distributive.
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!
i didnt understand how he did the e question on 2:58, please help me
On problem E, you will be using the distributive property twice. After you do 4(m+7) and distribute that, go on to the next part of this problem. Since a subtraction sign is in front of the 6, problem would now be -6(4-m). Once you finish distributing in that part of the problem, you would put all of your answers into a problem. That would become 4m+28-24+6m. We would use a subtraction sign in between 28 and 24 because we distributed with a -6 and the answer to -6*4 would equal -24. From there, you would combine the like terms. 4m and 6m are like terms. Since there is an addition sign before the 6m, you would do 4m+6m which equals 10m. 28 and 24 are also like terms. Since there is a subtraction sign before the 24, you would do 28-24. That would become 10m+4. You combine like terms because it makes the problem simpler. Combining like terms will be a way to get the simplest form of an answer. For more on combining terms, look up Combine Like Terms on Khan Academy. I hope this helps.
Two negatives become a positive abd you keep the variable.
Please vote for me
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?
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.
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?
No there isn't a order on doing it but it is still complicating.So I agree with you.
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*.
Give a thumbs up SALS AWESOME. He helps with everything. Anyway, isn't a variable only X and not Y or M.


Thanks
anything could be a variable. a variable represents and unknown number
Did anybody see the opening ceremony for the london 2012 olympics.
Can Sal please make a video on reverse distributive property?
Just look for the _*greatest common factor*_, that's all you need to do, I promise! ;-)

It's sometimes called _*factoring*_ ( or "_*taking out*_" ) , that's why you initially might not have found it.
There's actually a couple of these videos on Khan Academy!
https://www.khanacademy.org/math/algebra/multiplying-factoring-expression/Factoring-simple-expressions/v/factoring-and-the-distributive-property-3
is sunlight matter
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...
I don't under stand what the fancy x means. Can anyone help me?
I think he is just using it as a variable, to express an unknown, or part of a mathematical property.
Why do you sometimes change the addition or subtraction to its opposite?
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.
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!
for the problem 11x+12/2 would the answer still be right if I put 5 1/2x+6?
Given:
11x + 12/2
Division property of equality:
11x + 6

The answer to your problem is 11x + 6 not 5 1/2x + 6
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.
so you put sand b together (ab) so thats multiplication right?Couldn't you just put a multiplication sign or a dot?
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.
A negative multiplied by a negative is always a positive.
I still don't get the difference between x and y
x = Independent Variable
y = Dependent Variable
The value of y depends on the value of x.
Is this correct?
In the first series of questions:
(b) 0.6(0.2x+0.7)
=0.6*0.2x+0.7
=0.12x+0.7

(d) 6-(x-5)+7
=6+7-(x-5)
=13-x-5
=8+x

(f) -5(y-11)+2y
=-5y-(-55)+2y
=-5y+55+2y
=-5y+2y+55
=-3y+55

Sorry I'm not good at math...
Thank you.
For the first question you must times your second term by 0.6 too. Also take care when multiplying a decimal - you need the same amount of numbers after the decimal point as in the two being multiplied - if both are one decimal point then need two decimal points in your answer.
Eg. =0.6*0.2x+0.6*0.7
=0.12x+0.42
The second question you must multiple the second term by -1 as well as the first -(x-7)= - x - -7= -x+7
What do the letters mean? I don't understand that.
they are variables .In this they are the unknown numbers
At 4:41 , Sal said that you divide 11x/3. What do you do if the division isn't even?
Okay so what if the problem is something like: -6x - 7(-5x + 8) = 118

Would you use the same process if there is two "x"'s? Do you combine them or multiply them?

Or am I in the completely wrong place to be asking these questions because to be honest I have no idea what my math homework is about.
The distributive property still applies because multiplication comes before addition/subtraction. You would get:
-6x+35x-56=118
29x=174
x=6
Why do they have to use letters instead of numbers? its very confusing
the letters represent numbers that we don't know yet.
At 0:49, why do we have to multiply first then ad? Wouldn't it be much easier to just ad then multiply?
Because of Order of Operations! (:
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
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
When will koalas finally conquer the world
Does this have anything to do with math??/
At the beginning of the video on his first example, did Sal define the variables so he could get an answer? You can't do that in algebraic expressions, though, can you?
Actually you can, you just can't arbitrarily decide to give a value to unknown variables. It might be easier for example rather than dragging an inexact number around for say sin 45 * cos 45 * tan 45 to say that some variable t = sin 45 * cos 45 * tan 45. With the understanding that I'm using t as a placeholder for that value, so I don't have to carry long decimal digits around, through each operation until the very end.
i'm not getting the m and the x thing
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]
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)
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.
first part question c? i did not get that at all
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.
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.
what does x and y and m and all that mean?
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!!!
Why did they create this rule!
:-(
To make many problems that this rule can apply to easier to solve
At 5:16 how does it become 1/3?
At 5:04, Sal rewrites the fraction with a -1/3 in front. (He factors the -1/3 out) In effect, he was just rewriting the expression as multiplication of -1/3 and the numerator.
Why do people say over instead of divide?
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.

Hope this answers your question!
why do you times both of them
Let's look at 2(1+3). This is like saying 2 times everything in parenthesis(1+3).
So we could either turn this into 2(4) with is 8 or 2(1) + 2(3)= 2 + 6 = 8.
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.
There is a video in the Algebra section called "What is a variable?
i understand distrubutive properties but how come sometimes when your distrubuting the signs change? (from adding to subtracting or the other way around?)
2:45

Where does he get the -1 from?
It's like he just adds it from no where
It is like saying x+3 = 1x+3. Although it is correct, the 1 is unnecessary.
At 2:30 why does he put second part in brackets (how would you do it without brackets? would that be wrong?) and how does 6(4 - m) turn into 24 + 6m? Why doesn't it stay 24 - 6m?
Brackets can often be replaced by parenthesis, its just a way of making something more readable and representing that certain operations need to be done in a specific order. (I.e. (2+4) [ (4+6) - 7(2) ] Technically values in brackets get calculated before multiplying or adding parenthesis outside brackets .)
As for how does 6(4-m) turn into 24+6m, it should be 24-6m. Distributive property 6*4 + 6*(-m). You get 24 and a negative times a positive is a negative. Good catch.
At 4:47, why result in c., so 11/2x + 6, wasn't simplified to 5.5x + 6? Is this inconsistent with the rules of mathematics?
In example [E] Why do we have to put a 1 there? Is it required?
Where can I learn about the "1" that is hiding in front of parenthesis when doing distributive problems. I hear Sal refer to it, but I have never heard it explained and I am up to early algebra and it is giving me problems when going from positive to negative. All help appreciated!
re-watch the video it shows it
So what would 4+2(x-5) answer be and how would you solve it?
To solve it, first distribute 2 to ( x-5 ). This will give you 2x - 10 . Now add this to 4 . When you do so, you will have 2x -10 + 4. Now combining like terms we get 2x - 6 .
How do u do question s w
Like this with exponents
When he was solving fraction C, he didn't explain why 11x/2 was not divided and stayed that way ?
Alright so why is sal using fractions and almost a decimal question, if the order is distributive property first, before fractions and decimals AND negative numbers
At 1:51, why is the 5 negative? How do you know a minus symbol from a "negative" symbol?
i have no idea how to do this i need help
this video was very interesting. but, i was kinda confused at the end.
What about questions like 2(36) for distributive property?
If this is in front of the easier things how is tis supposed to help? Wouldn't it just confuse us more? Since it has so many variables wouldn't we learn it later? As review? Or a step up from what we're learning in this list?
Can you tell me what exactly you need help with/are talking about. I can help you better/understand you better if i had more information!

Thanks sweetie!

Hope this helped! :D
how come math has to have letters in it?
Letters are mainly used in math to simply show that they can mean any number. These letters are referred to as variables. Hope this helps.
in math if there are letters that ='s numbers, why don't people just put the numbers instead of the letters...i don't get the point. :(
Because sometimes we don't know the number instead of a number like txt=4 we can figure out t =2 but until than we use a letter oh and also don't use O because then it looks like a zero. I hope that answers your question.
I need a math problem for variable substituition (adding, substracting, multiply and dividing.
Also, I need a math problem for verbal expressions (adding, substracting, multiply, and dividing).
l
At the start of 3:05 in the video I got confused HELP
I really don't understand negative numbers. Its so confusing!!!!
what does a,b,c mean are they seceret code for 1,2,3.Also what is x 24.Just what do the letters mean this is math not spelling pluse i have no idea what the letters are for.
It is math, not spelling, the letters represent unknown values, they are called variables, they are a mathematical tool used VERY often in algebra. Calm down.
At 4:20

How did Sal turn (8x+12)/4 into 1/4(8x+12) - what are the rules behind this?
At 4:50 why didn't Sal divide 11 by 2, he just left it as 11/2 x...are you not allowed decimals?
randel24, I remember when I was in school, they made me do the same thing - convert to decimals - which I found to be very tedious. It's not really necessary to convert unless you must have an answer in decimal form. (As far as I understand, at least.)
So, Is it the sum of ( b+c) or is it a+(b) and then a + (c)?
@ GGBeischel: At 0:53, when Sal is explaining how to do 5(7+3), he says you can evaluate it either way, but 5(7)+5(3) is using the distributive property.
Couldn't you also use the distributive property on (8x+12)/4 as 4(2x+3)/4, then cancel the 4s in the numerator and denominator and be left with 2x+3?
I don`t understand algebra. a little help
In algebra, there are variables, or letters that represent an unknown value, that you have to solve. For example, in 4x=12, x equals 3.
What would you do if you got this problem on something such as the state test?:
Show 4(8+3), using distributive property, would you write: (4 * 8) + (4 * 3), or 32+12
?
Why is there pre-algebra in this video?
were did you get the 50?I do not under stand.
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
im confused what are the m + 28 and all that stuff i do not get any thing he is syaing :(
Thanks $ ur help you were a great help now i understand all well (most) of what he is saying......hope you can help me out more when i need it....can you plz tell me in my last post if you liked it and comment on it .......and one more thing i know all of you people out their are like on diffrent lessons than i am....well you can still look at mine and comment on it.... I just got started on this perogam 3-4 weeks ago :) and my math teacher mrs. Stuchman made me :(
Why do you multiply 1/2x and 1/2y?
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