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The distributive law of multiplication over addition says that if x, y and z are any numbers, then

x(y+z) = xy + xz

. It's true not only for integers, but also for real numbers or even complex numbers.

Here's a proof / graphical explanation:

__________

|*****|***| ^

|*****|***| |

|*****|***| |x

|*****|***| |

|*****|***| v

---------------

<--y--><-z->

Consider the ASCII rectangle above. It has height x and width y+z, therefore its area is x(y+z). Alternatively, it can be viewed as two smaller rectangles joined together. The one on the left has height x and width y, so its area is xy. Similarly, the one on the right has area xz. So the total area is xy + xz. Therefore x(y+z) = xy + xz.

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Q: What is the distributive property of multiplication over addition?
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What is the distributive property for addition?

Addition, by itself, does not have a distributive property. Multiplication has a distributive property over addition, according to which: a*(b + c) = a*b + a*c


What is the distributive property for multiplication?

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Numbers do not have a distributive property. The distributive property is an attribute of one arithmetical operation over another. The main example is the distributive property of multiplication over addition.


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What properties do the distributive property work for?

addition and subtraction * * * * * No. The distributive property applies to two operations, for example, to multiplication over addition or subtraction.


What is the distributive property in addition?

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What property involves multiplying a sum by a number?

The distributive property of multiplication over addition.


What is the name of the property that is used to say that 2(5 plus 3) is the same as 2 x 5 plus 2 x 3?

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What combines multiplication and addition by multiplying each addend by the number and adding the products?

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What does distributive property mean in math?

The distributive property of multiplication over addition states that a*(b + c) = a*b + a*c that is, the multiplication of the bracket by a can be distributed over the elements inside the bracket.


Should be distributive property of addition and multiplication have the same answer?

Yes, the Distributive Property is true over addition and multiplication, and it will continue to until you start studying exotic concepts such as Ring Theory or Field Theory.