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Distributive property example 1

ck12 Distributive Property example

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.
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.
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.
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!
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.
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
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 :)
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 :)
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.
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.
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 =
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)
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.
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!
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.
Two negatives become a positive abd you keep the variable.
Please vote for me
Whats the difference between associative, communitive and distributive.
Commutative-The order of the numbers in multiplication or addition doesn't matter.

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.

Distributive-A number multiplied by two or more addends together is that number multiplied by each addend separately.

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!
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 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...
Give a thumbs up SALS AWESOME. He helps with everything. Anyway, isn't a variable only X and not Y or M.

anything could be a variable. a variable represents and unknown number
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.
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.
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*.
How do you solve this?
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.
Did anybody see the opening ceremony for the london 2012 olympics.
for the problem 11x+12/2 would the answer still be right if I put 5 1/2x+6?
11x + 12/2
Division property of equality:
11x + 6

The answer to your problem is 11x + 6 not 5 1/2x + 6
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!
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.
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.
When will koalas finally conquer the world
Does this have anything to do with math??/
Simplify the following expression:


Distribute the −2 into the first set of parentheses:



Distribute the 7 into the parentheses:



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


Combine the m terms:


Combine the numeric terms:


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.
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!
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! (:
Why did they create this rule!
To make many problems that this rule can apply to easier to solve
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.
At 4:41 , Sal said that you divide 11x/3. What do you do if the division isn't even?
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!!!
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
A negative multiplied by a negative is always a positive.
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]
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.
What do the letters mean? I don't understand that.
they are variables .In this they are the unknown numbers
Why do they have to use letters instead of numbers? its very confusing
the letters represent numbers that we don't know yet.
At 4:35, could the improper fraction 11/2x be converted into 5 1/2x + 6?
Could I do that same thing with four numbers i.e a(b+c+d).
Then how can I do a/(b+c)=?
Please someone help me.
Multiplication is distributive, so sure you can say a(b+c+d) is the same as ab + ac + ad. Put in some numbers and try it. 1 (2+3+4) = 1 (9) =9. 1(2) + 1(3) + 1(4) = 2 + 3 + 4 = 9.

Division is not distributive so you cannot say that a/(b+c) = a/b + a/c. Just put in some numbers and see for yourself. 1 / (2 +3) = 1/5. Does 1/5 = 1/2 + 1/3? No, because 1/2 and 1/3 alone are both bigger than 1/5.
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.
Isn't he skipping the exponents?
Why do you multiply 1/2x and 1/2y?
what happens with a variable?
Can someone help me with this question??
3(2x – 5) – 2(4x + 1) = –5(x + 3) – 2
6x - 15 - 8x - 2 = -5x - 15 - 2
6x - 8x + 5x = -15 - 2 + 15 + 2
3x = 0

Ok, this might seem like a simple answer to my question; but how do you solve 9(96) with the distributive property? I know that the answer is 864....please help!!
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?
where did you get the -1? at exercise e).
thanks for the help =)
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.
How does -1 times -6m become +6m I do no understand.
negative times negative is positive.Positive times negative is negative
how come at 1:58 he got eight did he add or is it subtract -5 and 7.
Question: On sample C: 6+(x-5) +7 you said a(b+c) = ab+ac which means you distribute the 6 to both (x and -5) but it doesn't seem like you did that on sample C. Why is that? i was under the impression that you would get 6+(x-5)+7 = 6x-30+7.
in truth the formula is 6 + 1(x-5) + 7 the one is hidden because no mater what you distribute you still get 6 + 1x - 5 + 7 so if you distribute the hidden one you remove the ( ) your answer can now be simplified 6+7+-5 +1x = 8 + 1x or 8+x. on another note you can only distribute through multiplication your trying to use the addition to distribute that wont work.
5(4x-3)+8= -2

show me how this is done
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.
In question e. How do the negative symbols become -1.
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
take nine from 6,10 from 9,50 from 40 how come?
the first time you did was it hard but the part that have 8*(5*6) that what i get.
It's 240, right?
Simplify parenthesis.
Why is there pre-algebra in this video?
What it there are two numbers in front of the parentheses such as
-a -b(x-y) c
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.
I do not understand how he got the answer, in the last problem E), of '-22+ 2/3'. I understand how he got '-22' but how/why '2/3'?
If just multiplying the number on the outside of the parentheses is the same as the distributive property then why do we learn the distibutive law?!
how do you solve if one or more variables are unknown
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.
First, distribute the x.
5x + 2x
You can simplify this further, as they are like terms. You get:

I hope hope this helps!
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?
A) Yes and B)yes. :)
what grade do you have to know this stuff by?
Ha, I mastered it and I'm in 4th
at 2:24 what does M mean ?
'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).
On the question 6+(x-5)+7, I'm confused as to how you're suppose to know when it's saying Minus 5 or Negative 5. That's where I always mess up at because I'm thinking its x minus 5, not negative 5..so confusing.
x-5 is the same as x + (-5). When using distributive property (especially in later algebra and further math) it's important to think a bit more abstract about negatives and these minus signs. He could have said x minus 5 and it would have meant the same thing.
what kind of property is 4x-2=2x+5 or how do you do it?
Misael, this is an algebraic equation and is WAAAAY beyond this level. But just for giggles, here's your answer: to find for x, subtract 2x from both sides to isolate the variable, which leave you with 2x -2 = 5. Then, add 2 to both sides, which leave you with 2x = 3. Divide both sides by 1/2. x = 3/2.

Hang in there!
are the other types of distributive property methods because my looks a little different. it looks like this -2(x-3)-3x =2 (2x+3)-4
Yes! This is still the distributive property, just with a little more spunk!

-2(x-3) - 3x = 2(2x+3) - 4

-Distribute the -2 in for the parentheses next to it. -2(x-3) = -2x + 6
-Distribute the 2 in for the parentheses next to it. 2(2x+3) = 4x + 6

-Now replace your parenthesis with these new binomials.

-2x + 6 - 3x = 4x + 6 - 4

- Now, combine your like terms! (This is the extra spunk part!)

-5x + 6 = 4x + 2

-Now, solve for x by first, adding 5x on both sides. 6 = 9x + 2.
-Now, solve for x by subtracting 2 on both sides. 4 = 9x
-Now, solve for x by dividing 9 on both sides. x = 4/9

All done!

Hope this helps! -Terrell
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 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?
this is difficult for some one my age can some boy help me please?
thank you Jordan Potts I really appreciate that!
How does -1 times -6 become +6m i'm confused ? :{
When you multiply a negative by a negative, the result is positive.
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.
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
i do not get how you do it with fractions
sorry but this kinda off topic but do you have the squre root for 5 graders
I don't understand wht you are talking about
hi everyone hows it going?
Review the "multiplying negative numbers" video. Two negatives multiplied together make a positive.

What is Sal referring to as "x" and "y"? can anyone explain or link to a video.

so confused?
X and Y are variables. In the problems he is doing, we know not what those variables equate to. For example, 2y+3x. Lets say that y is equal to 1 and x is equal to 2. 2*1+3*2=8.
This video stunk! Sal was acting like he didn't have to explain anything cause we already knew it. I didn't get the video because I had no idea what he was talking about on e and the problems after e. There should be a video before this that doesn't have such complicated stuff.
Leah, there are a couple videos about the distributive property before this one. If you haven't seen them, why not watch them and then review this video again. If you still have questions, I'm happy to help. Don't let it fluster you.
In line with the distributive property I have seen a problem floating about the internet.

48 / (2(3*4) = X

Does the distributive property apply to this question, resulting in 48 / 48 = 1 ? Or does the placement of the parentheses or another reason affect the application of this property, resulting in 48 / 24 = 2 ?
i understand distrubutive properties but how come sometimes when your distrubuting the signs change? (from adding to subtracting or the other way around?)
It was so confusing! please help me out i don't get this sooo please help
why do they show it so slowly?
good question. look up.
what does a and b and c and d and e and f mean?
Those are variables. A variable is usually a letter, which can stand for any number. They are used in equations or in properties.