Arithmetic properties
The distributive property
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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!
Discussion and questions for this video
 Let's do some problems with the distributive property.
 And the distributive property just essentially reminds us
 that if we have, let's say, a times b plus c, and then we
 need to multiply a times this, we have to multiply a times
 both of these numbers.
 So this is going to be equal to a times b plus a times c.
 It will not be just a times b then plus c.
 And that makes complete sense.
 Let me give you an example.
 If I had said 5 times 3 plus 7, now, if you were to work
 this out using order of operations, you'd say, this is
 5 times 10.
 So you'd say, this is 5 times 10, which is equal to 50.
 And we know that that's the right answer.
 Now, use the distributive property, that tells us that
 this is going to be equal to 5 times 3, which is 15, plus 5
 times 7, which is 35.
 And 15 plus 35 is definitely 50.
 If you only multiplied the 5 times the 3, you'd have 15,
 and then plus the seven, you'd get the wrong answer.
 You're multiplying 5 times these things, you have to
 multiply 5 times both of these things.
 Because you're multiplying the sum of these guys.
 Anyway.
 Let's just apply that to a sampling of these problems.
 Let's do A.
 So we have 1/2 times x minus y minus 4.
 Well, we multiply 1/2 times both of these.
 So it's going to be 1/2 x minus 1/2 y minus
 4, and we're done.
 Let's do C.
 We have 6 plus x minus 5 plus 7.
 Well, here there's actually no distributive
 property to even do.
 We can actually just remove the parentheses.
 6 plus this thing, that's the same thing as 6 plus x plus
 negative 5 plus 7.
 Or you could view this as 6 plus So this
 right here is 2, right?
 Negative 5 plus 7 is 2, 2 plus 6 is 8, so it
 becomes 8 plus x.
 All right.
 Not too bad.
 That was C.
 Let's do E.
 We have 4 times m plus 7 minus 6 times 4 minus m.
 Let's do the distributive property.
 4 times m is 4m plus 4 times 7 is 28.
 And then we could do it two ways.
 Let's do it this way first. So we could have minus
 6 times 4 is 24.
 6 times negative m is minus 6m.
 And notice, I could have just said, times negative 6, and
 have a plus here, but I'm doing it in two steps.
 I'm doing the 6 first, and then I'll do the negative 1.
 And so this is going to be 4m plus 28, and then you
 distribute the negative sign.
 You can view this as a negative 1 times all of this.
 So negative 1 times 24 is minus 24.
 Negative 1 times minus 6m is plus 6m.
 Now you add the m terms. 4m plus 6m is 10m.
 And then add the constant terms. 28 minus 24, that is
 equal to plus 4.
 Let's go down here.
 Use the distributive property to simplify
 the following fractions.
 So I'll do every other one again.
 So the first one is, a is 8x plus 12 over 4.
 So the reason why they're saying the distributive
 property, you're essentially saying, let's divide this
 whole thing by 4.
 And to divide the whole thing by 4, you have to divide each
 of the things by 4.
 You could even view this as, this is the same thing as
 multiplying 1/4 times 8x plus 12.
 These two things are equivalent.
 Here you're dividing each by 4, here you're
 multiplying each by 4.
 If you did it this way, this is the same thing as 8x over 4
 plus 12 over 4.
 You're kind of doing a adding fractions problem in reverse.
 And then this 8 divided by 4 is going to be,
 this'll be 2x plus 3.
 That's one way to do it.
 Or you could do it this way.
 1/4 times 8x is 2x, plus 1/4 times 12 is 3.
 Either way, we got the same answer.
 C.
 We have 11x plus 12 over 2.
 Just like here.
 We could say, this is the same thing as 11 We could write
 it as 11 over 2x, if we like.
 Or 11x over 2, either way.
 Plus 12 over 2 plus 6.
 And let's just do one more.
 E.
 This looks interesting.
 We have a negative out in front, and then we have a 6z
 minus 2 over 3.
 So one way we can view this, this is the same thing, this
 is equal to, negative 1/3 times 6z minus 2.
 These two things are equivalent.
 Right?
 This is a negative 1/3.
 You could imagine a 1 right out here.
 Right?
 Negative 1/3 times 6z minus 2.
 And then you just do the distributive property.
 Negative 1/3 times 6z is going to be minus 2z.
 And then negative 1/3 times negative 2, negatives cancel
 out, you get plus 2/3.
 And you are done.
Be specific, and indicate a time in the video:
At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?

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This discussion area is not meant for answering homework questions.
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.
X and Y are called variables  I often replace them simply with question marks, as it is less confusing for me. X and y represent an unknown number that could really be any number at all. So you don't have to worry about finding out what the mean.
I think you should watch the video "Why all the letters in Algebra". I hope it will help with your confusion.
If you are having an equation like 7xY=56, the Y is the variable. When you are in a math problem and they have variables, you do the inverse operation to solve for the variable. To find what times 7 = 56, you have to divide 56 by 7 and Y will equal 8.
x & y are both variables used often in math, like in algebra. they are also used in graphing.
x and y are just variables, otherwise unknown if you don't give then values like
x = 7
y = 5.50967
x = 7
y = 5.50967
x and y are variables that have an unknown value
x and y are variables. Variables represent unknown values. They can pretty much be assigned to anything. So let's say you have a question like this:
What is the value of a in the following statement?
a(4) = 24
We know that 6 x 4 = 24, therefore a = 6 in the statement.
What is the value of a in the following statement?
a(4) = 24
We know that 6 x 4 = 24, therefore a = 6 in the statement.
x and y are variables which represent unknown values.
x and y is called unknown quantity.
x and y are variables that can be assigned a value.
They are just common variables.
He is referring to an unknown number as a letter
X and Y are used by professors, scientists and other people to represent an unknown number. You can use whatever letter you want, but x and y are 'traditional', if you pardon my pun:)
In 0:08 or another place
how did he do it without a paper that is impossible
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.
Yes just distributive property
When you did problem c. 6+(x5)+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.
He did... There is a "1" after the "6+" in other terms, before the parenthesis, and this "1" performs the distributive property. The thing is: whatever numbers, letters...etc. multiply "1" equal to this numbers, letters...etc. Ex: 6+1(x5)+7= 6+x5+7
This is what they did: (1*x)+(1*(5)).
This is what they did: (1*x)+(1*(5)).
The Distributive Property does not apply unless the terms in parentheses are being multiplied. If the problem were 6(x5)+7, then you would distribute and get 6x30+7=6x23. However, there is a plus sign in front of the parentheses.
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.
There variables.
All those letters are actually standing or representing the unknown.
Ex. 7 + x = 10. We are trying to find out the value of (x).
Letters are used because numbers would be too confusing.
Ex. 7 + x = 10. We are trying to find out the value of (x).
Letters are used because numbers would be too confusing.
yes because variables can be any number or symbol
not just algebra in problems also dummy's
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.
well you can't divide evenly. =)
Is there a reason for this beyond not liking the looks of decimals in the equations? I personally have a more intuitive grasp of decimals over fractions, fractions where always my biggest problem in school and I hated dealing with them.
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)
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)
We use variables when we are talking about a particular TYPE of mathematical problem, which covers many different examples of individual problems. For example, if Sal were to talk about adding the fractions 1/2 and 1/3, that would be a good example of adding fractions. But what if you wanted to add the fractions 2/3 and 74/17? Would Sal's example apply to your problem? Both Sal's fractions had a 1 in the numerator, which yours don't. Both Sal's fractions were less than 1, and one of yours isn't. So you're not sure. But if we use variables instead, we can give the example of adding the fractions a/b and c/d, and we can further specify that a and c can be any integers, and b and d can be any positive integers. Now we can be sure that the example applies to our own problem, because using variables allowed us to give a general example rather than a very specific one.
It is not a requirement for him to use them, however if he uses them it gets you used to them because as you get into harder math the x & y are variables that will come up in almost every problem.
We use variables when we are talking about a particular TYPE of mathematical problem, which covers many different examples of individual problems. For example, if Sal were to talk about adding the fractions 1/2 and 1/3, that would be a good example of adding fractions. But what if you wanted to add the fractions 2/3 and 74/17? Would Sal's example apply to your problem? Both Sal's fractions had a 1 in the numerator, which yours don't. Both Sal's fractions were less than 1, and one of yours isnt
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(11.035) 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?
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(11.035) 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(11.035) = d  1.035d, we also know that it works in the other direction, so d  1.035d = d(11.035). 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(11.035). I hope I answered your question. If not, I apologize.
What is unique about the distributive property though, is that it works in both directions. Essentially since we know that d(11.035) = d  1.035d, we also know that it works in the other direction, so d  1.035d = d(11.035). 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(11.035). I hope I answered your question. If not, I apologize.
thank you so much teddy
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 :)
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 :)
You won't use Algebra in real life, however studying algebra actually makes you smarter (it's like working out your brain and forming new connections) therefore it makes you better at everything else. So you'll be better at things you do enjoy :)
If you want to learn more about taxes, bills and buying houses, there are already videos about those topics here: https://www.khanacademy.org/economicsfinancedomain/corefinance. If you go through those videos, you're going to find that you need to know the distributive property, algebra and even more.
You're not alone in wondering why math is so boring. Millions of people find math boring. I was one of them. I used to hate math even though I made it all the way to AP Calculus in high school with good grades. I only got through it because I wanted to get good grades, but math classes made me miserable. I couldn't wait to graduate from high school so I could forget about math forever.
I don't feel that way anymore. I wish I could go back in time and teach my high school self to become more passionate and interested in math. I would have had a better experience instead of being so miserable.
I love math now. I think math is one of the most awesome and amazing things in life. It's the language of science, nature, money and so much more. I care about math so much that I wrote this long response to share my love for math and to prevent people like you from going through the agony I went through.
There's no secret to how I fell in love with math. It just took time and effort. I read books about math. I signed up for Khan Academy, watched the videos, did the exercises and kept learning. I even watched movies about math. The more I learned, the more I fell in love with what I was learning.
If you want something to be interesting, you have to get interested in what you're doing. You need to find ways to fall in love with math and become passionate about it. Nobody can do that for you. Your teachers can't do it. Khan Academy can't do it. It's really up to you if you want the rest of your math classes to be boring and miserable like mine were, or to make math one of the most awesome and amazing things in your life. Thanks for your honesty and taking the time to read my response.
You're not alone in wondering why math is so boring. Millions of people find math boring. I was one of them. I used to hate math even though I made it all the way to AP Calculus in high school with good grades. I only got through it because I wanted to get good grades, but math classes made me miserable. I couldn't wait to graduate from high school so I could forget about math forever.
I don't feel that way anymore. I wish I could go back in time and teach my high school self to become more passionate and interested in math. I would have had a better experience instead of being so miserable.
I love math now. I think math is one of the most awesome and amazing things in life. It's the language of science, nature, money and so much more. I care about math so much that I wrote this long response to share my love for math and to prevent people like you from going through the agony I went through.
There's no secret to how I fell in love with math. It just took time and effort. I read books about math. I signed up for Khan Academy, watched the videos, did the exercises and kept learning. I even watched movies about math. The more I learned, the more I fell in love with what I was learning.
If you want something to be interesting, you have to get interested in what you're doing. You need to find ways to fall in love with math and become passionate about it. Nobody can do that for you. Your teachers can't do it. Khan Academy can't do it. It's really up to you if you want the rest of your math classes to be boring and miserable like mine were, or to make math one of the most awesome and amazing things in your life. Thanks for your honesty and taking the time to read my response.
where did you get the 1? at exercise e).
Because when you have (Example) (4x5) is the same as (1)(4x5), so in the question that Sal does its: (246m) is the same as 1(246m) or (1)(246m). This causes you to change all the signs within the brackets.
Yes please. I still don't understand.
can you be more specific please?
when your doing e, why do you put parenthesis around 246m 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.
Could have just said 24+6m without parenthesis.
hmmmm....i do know but I just need to get better at the problems so I could do the problems
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
6 + x  12 ?
if it is a negative it becomes
6 + x. 2
I am confuse on this part too
Minus and Negative is the same.
Let us rewrite the problem:
6+(x5)+7 = 6+ 1(x  5) +7
= 6 + (1 . x)  (1 . 5) + 7
= 6 + x  5 + 7
6+(x5)+7 = 6+ 1(x  5) +7
= 6 + (1 . x)  (1 . 5) + 7
= 6 + x  5 + 7
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.
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 =
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(4m). 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(4m)... 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...2824 = 4...So your answer is 10m + 4
Hope that helps!
Hope that helps!
i get it well you say like that its easy
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 x5 first, meaning before 57? 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!
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!
Thank you very much!!!! Now everything makes sence!
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.
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.
Thanks! This was more simple than I had thought it would have been. ;D
1:14 what does sampling mean?
Definition: a small part or quantity intended to show what the whole is like.
Sampling means a small quantity to show the entire basis of the thing you are trying to find what it 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 dailylife 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!
However, that's much for a much later time. The uses of this simple distributive property are more dailylife 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.
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.
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.
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.
CommutativeThe order of the numbers in multiplication or addition doesn't matter.
Examples:
1+2=2+1
27*8=8*27
AssociativeThe 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)
DistributiveA 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*(21+3)=4*(2+(1)+3)=4*2+4*1+4*3=4*24*1+4*3
6*(5634)=6*566*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!
Examples:
1+2=2+1
27*8=8*27
AssociativeThe 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)
DistributiveA 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*(21+3)=4*(2+(1)+3)=4*2+4*1+4*3=4*24*1+4*3
6*(5634)=6*566*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(4m). Once you finish distributing in that part of the problem, you would put all of your answers into a problem. That would become 4m+2824+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 2824. 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
Please vote for me
that is not true
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?
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.
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.
wht is six x
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
Thanks
anything could be a variable. a variable represents and unknown number
It can be anything other than a number!@@#$%^&*(()_+_';123456!#$%6
Thank You SALS STILL AWESOME
A variable can be _anything_. Any number _or_ letter.
Did anybody see the opening ceremony for the london 2012 olympics.
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...
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...
Why are you asking this question on a math video about the distributive property?
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
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.
He just wanted to show us the other ones thats why he skiped letter d
He felt like it for no good reason
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.
Thank you because i was confused about that
A negative multiplied by a negative is always a positive.
Yes, you are correct. :)
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.
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(x5)+7
=6+7(x5)
=13x5
=8+x
(f) 5(y11)+2y
=5y(55)+2y
=5y+55+2y
=5y+2y+55
=3y+55
Sorry I'm not good at math...
Thank you.
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(x5)+7
=6+7(x5)
=13x5
=8+x
(f) 5(y11)+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 (x7)=  x  7= x+7
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 (x7)=  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?
You have a decimal on 4:41
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.
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+35x56=118
29x=174
x=6
6x+35x56=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.
They're a.k.a incognites...
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
(7)(m+3) = 7m+21
When will koalas finally conquer the world
Does this have anything to do with math??/
That was a random comment Eric Harvey and what does koalas have to do with math??
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]
thanks for the help
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(4m)
I'm talking about the expression 4(m+7)6(4m)
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.
amazing! I've cogitated that hypothesis and you help me to make sure. Thanks a lot!
what does x,m,z,and y mean?
They are variables. They represent numbers of unknown value.
they are just symbols
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.
under 5 + 7, why did he put 2? i think thats it...thanks
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.
−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!!!
If you get this video, it's just a matter of time and practice before you are acing calculus!!!
ohh.. okay. thanks
Yes, we don't know what numbers x,y and m are. Try watching the first algebra videos to really understand it. :)
does each one have a specific meaning?
x,y and m are variables(unknown values)
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!
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.
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 don't get how to do e!
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
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.
"(246m) is exactly the same thing as saying 1(246m)."
Is there a video that explains WHY?
I don't like just memorizing arbitrary concepts like "([whatever]) = 1([whatever])"
Is there a video that explains WHY?
I don't like just memorizing arbitrary concepts like "([whatever]) = 1([whatever])"
Sal is trying to explain how to distribute the negative symbol to the numbers inside the parenthesis. (246m) is exactly the same thing as saying 1(246m).
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(4m) turn into 24+6m, it should be 246m. Distributive property 6*4 + 6*(m). You get 24 and a negative times a positive is a negative. Good catch.
As for how does 6(4m) turn into 24+6m, it should be 246m. 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!
rewatch the video it shows it
Hi!!
Before I directly answer your question, let me brush up on a few multiplication facts for you....
Remember that:
``` 1 * n = n ```
This is when n is any number. If you multiply anything, and I mean *anything* by 1, you are going to get that number as your answer. Why? Because when we talk of multiplication we are talking in groups. So you can have 1 group of that number, or your can have that number of groups of 1.
For example, if you have 1 x 8 , you can think of it as one group of 8 items. If you have 8 x 1, you can think of it as 8 groups of 1 item. So, at the end of the day, you get a product of 8. Why? Because any number multiplied by 1 is going to give you that number.
Hopefully that makes sense, because it is vital you understand the identity property of multiplication (that's what its called when you multiply by 1) to understand the "hidden 1" of the distributive property.
Why you ask? Because that is exactly what is happening in the distributive property! You have your number, and you are multiplying it by 1. Let me explain a bit more:
If you have a number, you can always write it as a multiplication problem. Why? Because it can always be written as itself times 1. What does that mean? It means that if you have any number (lets say 13), you can multiply it by 1 and have a valid multiplication problem that makes that number. What that means, is that I can say 13 = 1 x 13. That is valid.
So... when we have the distributive property, that is basically what we are calling our "hidden 1." I showed that 13 is the same thing as 1 x 13. The 1 that I multiplied the 13 by, is what Sal is calling the "hidden 1." It doesn't show, because we can reduce 1 x 13 to be 13, which is much simpler, by it is still there.
Now, when we have distributive properties, its the same thing except the hidden 1 is on the outside of the parenthesis. Why? Because one is divisible into everything.
So if we have the problem (5 + 3) and we want to make is negative, we can take out that "hidden 1" and put it in front of the parenthesis:
1(5 +3)
Then, we make the 1 negative:
1 (5 + 3)
and solve:
1 (8)
8
Now how do we know we can put that one there? Because we can write the equation of (5 + 3) as:
(1 x 5 + 1 x 3)
Using the distributive property, we see that the one can be put on the outside to make a simpler equation: 1 (5 + 3)
Hope this helps!! If you would like, I can show you more complex equations as well. :)
Sylvia.
Before I directly answer your question, let me brush up on a few multiplication facts for you....
Remember that:
``` 1 * n = n ```
This is when n is any number. If you multiply anything, and I mean *anything* by 1, you are going to get that number as your answer. Why? Because when we talk of multiplication we are talking in groups. So you can have 1 group of that number, or your can have that number of groups of 1.
For example, if you have 1 x 8 , you can think of it as one group of 8 items. If you have 8 x 1, you can think of it as 8 groups of 1 item. So, at the end of the day, you get a product of 8. Why? Because any number multiplied by 1 is going to give you that number.
Hopefully that makes sense, because it is vital you understand the identity property of multiplication (that's what its called when you multiply by 1) to understand the "hidden 1" of the distributive property.
Why you ask? Because that is exactly what is happening in the distributive property! You have your number, and you are multiplying it by 1. Let me explain a bit more:
If you have a number, you can always write it as a multiplication problem. Why? Because it can always be written as itself times 1. What does that mean? It means that if you have any number (lets say 13), you can multiply it by 1 and have a valid multiplication problem that makes that number. What that means, is that I can say 13 = 1 x 13. That is valid.
So... when we have the distributive property, that is basically what we are calling our "hidden 1." I showed that 13 is the same thing as 1 x 13. The 1 that I multiplied the 13 by, is what Sal is calling the "hidden 1." It doesn't show, because we can reduce 1 x 13 to be 13, which is much simpler, by it is still there.
Now, when we have distributive properties, its the same thing except the hidden 1 is on the outside of the parenthesis. Why? Because one is divisible into everything.
So if we have the problem (5 + 3) and we want to make is negative, we can take out that "hidden 1" and put it in front of the parenthesis:
1(5 +3)
Then, we make the 1 negative:
1 (5 + 3)
and solve:
1 (8)
8
Now how do we know we can put that one there? Because we can write the equation of (5 + 3) as:
(1 x 5 + 1 x 3)
Using the distributive property, we see that the one can be put on the outside to make a simpler equation: 1 (5 + 3)
Hope this helps!! If you would like, I can show you more complex equations as well. :)
Sylvia.
help!
How do u do question s w
Like this with exponents
Like this with exponents
that is easy man
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
id like to have some help
How do you do this
this video was very interesting. but, i was kinda confused at the end.
what grade mathe is this
it is 6th or 5th
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
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
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.
a,b, and c are variables. They can be *any* number (although I like the secret code theory). In fact, in the provided example, X is a variable as well. Let me explain.
Variables are usually letters (although they can be anything, smiley faces, symbols etc.). They stand for a number in an equation that you have not yet solved for. For example, if you had x24, it means that some number that you don't know yet, is being multiplied by 24. x could stand for 2, 5, 10.579, any number.
So if I had 5X = 50, and I had to solve for X. I would look at this and think...
"What times 5 equals 50 (in other words what does X equal). 5 times 2 = 10, so X does not equal 2 because I want it to equal 50. 5 times 5 equals 25, so X does not equal 5. But what about ten? 5 times ten equal 50! therefore, X must equal 10!"
A simpler way to do this is to divide 50 by 5. That would immediately give you 10 because 5 goes into 50, 10 times.
I hope this has helped you understand what variables are.
Variables are usually letters (although they can be anything, smiley faces, symbols etc.). They stand for a number in an equation that you have not yet solved for. For example, if you had x24, it means that some number that you don't know yet, is being multiplied by 24. x could stand for 2, 5, 10.579, any number.
So if I had 5X = 50, and I had to solve for X. I would look at this and think...
"What times 5 equals 50 (in other words what does X equal). 5 times 2 = 10, so X does not equal 2 because I want it to equal 50. 5 times 5 equals 25, so X does not equal 5. But what about ten? 5 times ten equal 50! therefore, X must equal 10!"
A simpler way to do this is to divide 50 by 5. That would immediately give you 10 because 5 goes into 50, 10 times.
I hope this has helped you understand what variables are.
I don't understand this
At 4:20
How did Sal turn (8x+12)/4 into 1/4(8x+12)  what are the rules behind this?
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.)
That means divide by 2
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 got it never mind
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
?
Show 4(8+3), using distributive property, would you write: (4 * 8) + (4 * 3), or 32+12
?
you would write (4*8)+(4*3)
Why is there prealgebra 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
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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