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Property of Real Numbers
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Property of Real Numbers

by RC
(Mesa, AZ)











































Fundamental Properties of Real Numbers

The Seven Fundamental Properties of Real Numbers are: Associative Property, Commutative Property, Distributive Property, Identity Property, Inverse Property, Closure Property, and Density Property.

Which property of multiplication is shown 1 × 5 + 9 × 5 = (1 + 9) × 5 ?


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Feb 02, 2013
Distributive Property
by: Staff


Answer

Part I

1 × 5 + 9 × 5 = (1 + 9) × 5

This is an example of factoring.

The property demonstrated in the example is the Distributive Property.

The Distributive Property combines two operations: multiplication and addition . It is formally defined as "the distribution of multiplication over addition".

There is only one Distributive Property which combines (both) addition and multiplication. There is not a separate Distributive Property for addition, and another Distributive Property for multiplication.

Generally, the Distributive Property is used to simplify an expression containing parentheses to an expression without parentheses. (However, the Distributive Property is also used to factor an expression such as 1 × 5 + 9 × 5.)

Using the example given in the problem statement:

(1 + 9) × 5 = 1 × 5 + 9 × 5

To evaluate the expression (1 + 9) × 5, you could add the 1 and the 9 together first, and then multiply by 5.

1 + 9 = 10

10 × 5 = 50

However, you can also multiply each of the two numbers by 5 separately, and then add the results together.

1 × 5 = 5

9 × 5 = 45

5 + 45 = 50

The results are the same either way.

The Distributive Law states that the following expressions are equivalent to one another:

(1 + 9) × 5 = 1 × 5 + 9 × 5 = 50


Mental Math


The Distributive Law is used simplify calculations using mental math. For example:

4 × 523 = ?

Using the Distributive Law, the number 523 can be arbitrarily spit into parts, and re-written as shown below. This is called Decomposing the Multiplier.

4 × 523 = 4 × (500 + 20 + 3)

4 × (500 + 20 + 3) = 4 * 500 + 4 * 20 + 4 * 3

= 2000 + 80 + 12

= 2092


Algebra

The Distributive Law is even more important in Algebra.

The variables used in algebra behave the same way numbers behave - because variables represent numbers.

When you understand arithmetic thoroughly, you automatically understand the mechanics of algebra.

The mechanics of Algebra (addition, multiplication, combining fractions, etc.) are exactly the same as the mechanics of arithmetic.

The Distributive Law allows you to simplify an algebraic expression without knowing the actual values represented by the variables.

The Distributive Law can be stated using algebraic notation as follows:

a * (b + c) = a * b + a * c

If more than three variables are used, the Distributive Law can be stated: a * (b + c + d + e + ... + z) = a * b + a * c + a * d + a * e + ... + a * z



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Feb 02, 2013
Distributive Property
by: Staff


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Part II

Here are some additional examples:

Math – Distributive Property - Examples







Thanks for writing.

Staff
www.solving-math-problems.com


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