Distributive property example 1
Distributive property example 1
- 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.
- 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.
- 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.
- 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.
- This is a negative 1/3.
- You could imagine a 1 right out here.
- 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.
Ex. 7 + x = 10. We are trying to find out the value of (x).
Letters are used because numbers would be too confusing.
Hope that helps!
6+(x-5)+7 = 6+ 1(x - 5) +7
= 6 + (1 . x) - (1 . 5) + 7
= 6 + x - 5 + 7
Could have just said -24+6m without parenthesis.
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.
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?
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.
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)
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 =
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.
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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 :)
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.
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!
Please vote for me
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!
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!
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...
This is what I did
-5 times y equals -5y+ -25=15y
but then do i add or subtract the 25 to both sides?
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.
I'm talking about the expression 4(m+7)-6(4-m)
If you get this video, it's just a matter of time and practice before you are acing calculus!!!
Like this with exponents
we went over this is class today and i was lost and we have homework over it and im still kinda lost
-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
Hope this helps! -Terrell
Show 4(8+3), using distributive property, would you write: (4 * 8) + (4 * 3), or 32+12
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!!
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.
4(m + 7) - 6(4 - m)
So we want to wind up with a simpler expression -- fewer terms and numerals. The 4 distributes across the "m" and the 7, and the six distributes across the 4 and the "m". The point is that when one number is multiplied by a parenthesized expression, the number outside the parentheses has to be multiplied by EVERY item inside the parentheses. So we get
(4m + (4x7)) - ((6x4) - 6m)
(4m + 28) - (24 - 6m)
4m + 28 - 24 + 6m <- the '-' outside the parens
distributes giving + 6m
(4m + 6m) + (28 - 24) <- rearranging and regrouping
10m + 4
The second "e" expression is
6z - 2
Which is the same as -1/3 x (6z - 2), as he points out in the video. So we just have to distribute the -1/3 across the rest of the expression. So we get
-1/3 x 6z - (-1/3 x 2)
-2z - (-2/3)
-2z + 2/3
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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When naming a variable, it is okay to use most letters, but some are reserved, like 'e', which represents the value 2.7831...
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This is great, I finally understand quadratic functions!
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