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big ideas math

by bob
(new orleans)











































the true equations show the associative properities of addition and multiplication why are they called associative write the properties

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Sep 03, 2010
Associative Law
by: Staff

The question:

by Bob
(New Orleans)

The true equations show the associative properties of addition and multiplication
Why are they called associative
Write the properties

The answer:

A true equation is a balanced equation. A true equation is mathematically accurate. The value on the left hand side is equal to the value on the right hand side of the equation. 3 + 5 = 8 is a true equation. 3 + 5 = 7 is not a true equation because 3 + 5 does not equal 7.

The fundamental properties of REAL NUMBERS are the: Associative Property, Commutative Property, Distributive Property , Identity Property , Inverse Property , Closure Property, and Density Property.

The Associative property is broken down into the Associative Law of Addition and the Associative Law of Multiplication.



Now let’s take a look at the Associative Law, as it applies to real numbers.

The Associative Law of Addition
The following example is a TRUE EQUATION because the value on the left is equal to the value on the right:

5 + 1 + 4 = 5 + 1 + 4

The Associate Law of Addition answers the question: does it make any difference in what order the numbers are added? The answer is no. The result is the same regardless of the order the numbers are added.

(5 + 1) + 4 = 5 + (1 + 4)


The Associative Law of Multiplication


The Associate Law of Multiplication answers the same question for quantities multiplied together: does it make any difference in what order the numbers are multiplied? The answer is no. The result is the same regardless of the order the numbers are multiplied.

5 * 1 * 4 = 5 * 1 * 4

(5 * 1) * 4 = 5 * (1 * 4)



Although you did not ask, what happens when + and * are mixed?

How do you evaluate the following type of equation?


5 + 1*4 = ?

What do you do first? Do you add the 5 and the 1 and multiply the result by 4? Or, do you multiply 1*4 and then add the 5?

The answer is often expressed in the acronym PEMDAS. This is the ORDER of OPERATIONS.

There isnt enough space to review that question here (we are limited to 3000 characters). At this point, just be aware that there is a correct order.




Thanks for writing.


Staff
www.solving-math-problems.com


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