Question 897612
name the property of real numbers illustrated by each equation.
2(3x-y)=6x-2y

3+(pi)=(pi)+3



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2(3x-y)=6x-2y ... <font color="blue">This is using the <font color="red">distributive property</font>


<a href="http://www.algebrahelp.com/lessons/simplifying/distribution/">Distributive Property</a>


Some other examples of the distributive property


<img src = "http://www.mathwarehouse.com/dictionary/D-words/distributive-property-diagramB.png">

(Image Source: http://www.mathwarehouse.com/dictionary/D-words/distributive-property-diagramB.png)


Notice how the outer term is being multiplied by <u>EVERY</u> term inside the parenthesis and then you add up those products. A common mistake is to multiply the outer term with only the first term inside (or only a few terms inside, but not all). Be careful not to fall for this common mistake.
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3+(pi)=(pi)+3 ... <font color="blue">This is using the <font color="red">Commutative Property of Addition</font>


<a href="http://coolmath.com/prealgebra/06-properties/01-properties-commutative-addition-01.htm">Commutative Property of Addition</a>


This property basically states: "You can add any two numbers in any order you want"


Other examples


7+11 = 18
11+7 = 18


9+8 = 17
8+9 = 17


44+6 = 50
6+44 = 50


You can use a number line to display each example visually.


I'm sure you are quite familiar with this property at this point on an intuitive/common sense level. The "Commutative Property of Addition" is just the term mathematicians have given the idea.

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