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Basic Math Properties (Order of Operations, Commutative, Associative, and Distribution Properties)

Basic Math Properties (Order of Operations, Commutative, Associative, and Distribution Properties)

Author: Kendra Wheeler
Description:

Basic math properties definitions and examples. Understanding algebra and how to simply or solve an equation.

Exampling the three basic properties and the order of operations.

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Tutorial

Order of Operations

 The order of operations is a technique for solving a problem. 

 The oder of operations is PEMDAS which stands for:

1.     Parentheses--- (        ) 

2.    Exponents--- (      )2  or   X2  ---The number 2 is the exponent

3.    Multiply-- 2*3

4.    Divide-- 2/3 

5.    Addition--- 2+3

6.    Subtraction-- 2-3

It is saying that parentheses out rank exponents which out rank multiply and divide which then these two out rank addition and  subtraction. 

A way to remember the order of operations is through a phrase: PEMDAS

Please Excuse My Dear Aunt Sally 

Remember : When working with multipication, division, addition and subtraction you work left to right ( just like reading a book).

 

Order of Operations Examples

Commutative Property

The commutative property refers to the word commute meaning you can move the numbers or values around. This property is only used for multiplying or addition. You can not use commutative property when dealing with division or subtraction. 

Examples :

1.  2 + 3 + 5 = 2 + 5 + 3 = 5 + 3 + 2 

2.  X * Y * Z = X * Z * Y = Y * Z * X 

Using the Commutative Property

You can work out examples using commutiative property. Try these problems by yourself using commutative property before pressing play. These examples are here to help you understand the concept.

Associative Property

 The associative property refers to the rule of grouping. 

 
For addition, the rule is "a + (b + c) = (a + b) + c"; in numbers, this means 

2 + (3 + 4) = (2 + 3) + 4. 

 

For multiplication the rule is "a(bc)= (ab)c" and in number this means 2(3x4)= (2x3)4.

 

 

Using the Associative Property

Work out these problems using associative property. Try to work out these problems before pressing play! These worked out problems using associative property are here to help you understand the concept.

Distribution Property

The distribution property means to taking a number or a variable through the parentheses or factoring something out. 

Examples: 

1. 6(2x + 3) = 12x + 18 -- This example was taking the number through the parentheses. 

 

2.  ( 6x - 18 ) = 6( x - 3 ) -- This example shows using distribution by factoring something out. In this case it was factoring out a 6. 

Using the Distribution Property

Work out these problems using the distribution property. Try these problems by yourself before pressing play! These worked out problems are here to help you understand the concept.