Question 409039

Basic Number Properties: 

{{{Associative}}},{{{Commutative}}}, and {{{Distributive}}}




The word "{{{associative}}}" comes from "associate" or "group";the {{{Associative}}} Property is the rule that refers to 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}}}"; in numbers, this means {{{2(3*4) = (2*3)4}}}.


The word "{{{commutative}}}" comes from "commute" or "move around", so the {{{Commutative}}} Property is the one that refers to moving stuff around. 

For addition, the rule is "{{{a + b = b + a}}}"; in numbers, this means {{{2 + 3 = 3 + 2}}}. 

For multiplication, the rule is "{{{ab = ba}}}"; in numbers, this means {{{2*3 = 3*2}}}. 



The {{{Distributive}}}Property is easy to remember, if you recall that "multiplication distributes over addition". Formally, they write this property as {{{a(b + c) = ab + ac}}}. In numbers, this means, that {{{2(3 + 4) = 2×3 + 2×4}}}. 


1.{{{ mn=nm}}}.........here you have  the {{{Commutative}}} Property-the rule for multiplication

2. {{{(3r+2)+s=3r+(2+s)}}}.....the {{{Associative}}} Property- the rule for {{{addition}}}

3. If {{{3x=15}}} then {{{15=3x}}}...the {{{Commutative}}} Property-the rule for multiplication