Can someone explain the distributive property in Algebra for me.?

Question

I am in eighth grade and am in an advanced algebra class but if I don't learn the distributive property I'm going to get ANOTHER F on the next quiz.

Answer 1

The distributive property involves multiplication and addition.

If we have 2(4+5) we have two ways to obtain the result:
first way: we add inside parenthesis 2(4+5)=2x9 = 18
Second way: we multiply and destroy the parenthesis 2x4 + 2x5 =8+10 = 18

From this comes the distributive property: a(b+c) = ab+ac
It means there are two ways for the calculation.

I do not know if this is sufficient for you.

Answer 2

The best way to explain the distributive property is with a diagram.

When you multiply two numbers, it's like making a rectangle with those two numbers, and finding the area, right? e.g., a rectangle with width 5 and height 4 has area 20.

.....5
-----------
|---------|
|---------| 4
|---------|
-----------

Now suppose instead of 5, you had something like 2 + 3.

...2....3
------------
|----|------|
|----|------| 4
|----|------|
------------

The area of the rectangle is still 20, of course. But we can also find the area of the two smaller rectangles, the 2x4 rectangle and the 3x4 rectangle. 2*4 is 8, and 3*4 is 12. The total area is 20.

This is the distributive property. If you're multiplying one thing by a sum of things, then you can multiply that one thing by each of those things in turn, and you'll get the same answer.

.b..c..d
---------
|--|--|--|
|--|--|--| a
|--|--|--|
---------

Area = a * (b+c+d), but area also = (a*b) + (a*c) + (a*d)

You can distribute the "a times" over the b, c, and d.

Or think about taxes. If I took 5% tax on a $2 burger, $1 fries, and $1 drink, I get 10 cents + 5 cents + 5 cents = 20 cents. But if I took a 5% tax on a $4 combo, I'll also get 20 cents. It's the same, whether you multiply by 5% first and then add those numbers, or if you add first and then multiply.

The opposite of the distributive property is factoring. If I have a*b + a*c + a*d, I can factor out the a and get a*(b+c+d).

Answer 3

The distributive property means that in an equation like:

A ( B + C )

The A gets "distributed" (handed out) to both the B and the C, so the results become:

AB + AC.

Let's use real numbers A=5, B=2, and C=3:

A ( B+C )
5 ( 2 + 3 )

becomes

AB + AC (final answer unless we know A, B, and C)

5*2 + 5*3 (Intermediate answer because we know A, B, and C)

10 + 15

25 (Final answer because we know A, B, and C )

I've included a websight that does a little more thorough job with this example.

Answer 4

The Distributive Property is an algebra property which is used to multiply a single term and two or more terms inside a set of parentheses. Take a look at the problem below.

2(3 + 6) = 2x3 + 2x6 = 6 + 12 = 18

Answer 5

The usual statement of the distributive rule is:

a(b + c) = ab + ac

When you remove parentheses, distribute a across both terms within the parentheses.

You must be careful with algebraic signs. For example,

3(x + 2) = 3x + 6

3(x - 2) = 3x - 6

-3(x - 2) = - 3x + 6

Keep on the lookout for patterns. If you see an expression of the form

ac + ab

you can factor out the a and write

a(b + c)

In other words

ab + ac = a(b + c)

which is the distributive rule read backwards ( the = sign means just that).

Answer 6

Allow me to show what's going on by doing an example:
Let's calculate 4*(5b+3g)

Think of the parentheses as a bag.
The bag contains five blue marbles and three green marbles.
You have four such bags.

How many blue marbles do you have? Well, if you have four bags, and each bag has five blue marbles, then you obviously have 4*5=20 blue marbles.
Similarly, you have 4*3 = 12 green marbles.

Therefore, 4*(5b+3g) = 20b + 12g

When you're distributing, you're just taking stuff out of the bag (the parentheses). If you have four bags, then you can take out everything from one bag, and multiply the amount of everything in that bag by four. That'll tell you how much stuff you have in all the bags put together.

That's all the distributive property really is. Hope that helps!

Answer 7

Having the property, in multiplication, that x(y+z) = xy + xz. The factor x is "distributed" across all the factors in the parentheses (in this case y and z).

The sight I have listed is a great math resource.

Answer 8

Check out the link below. About 1/3 of the way down on the page is a very easy explanation of the distributive property. I hope that this helps you.

http://www.wtamu.edu/academic/anns/mps/math/mathlab/beg_algebra/beg_alg_tut8_property.htm

Answer 9

It has to do with the equation sign, what ever sign is to the left of the equation sign changes to its opposite on crossing the equation sign and visa versa. ex. 5*x=30, x=30/5, 6+y=10. y=10-6, hope thats clear,the -6 would be +6 changing it back to the left and /5 would be5* changing it back to the left.

Answer 10

http://www.algebrahelp.com/lessons/simplifying/distribution/ try using this link..or look up the distrubutive property on google or any other search engine ...It is basically taking the number outside of the parentheses and multiplying the digits inside by that number...Good luck!