Question 487933
The "Commutative Laws" say you can swap numbers over and still get the same answer ...

... when you add (a + b  =  b + a)  or when you multiply (a * b  =  b * a)

{{{Commutative}}}{{{ Laws}}}: 
	
a + b  =  b + a
a * b  =  b * a


The "Associative Laws" say that it doesn't matter how you group the numbers (i.e. which you calculate first) ...

... when you add (a + b) + c  =  a + (b + c)  or when you multiply (a * b) * c  =  a * (b *c)

{{{Associative}}}{{{ Laws}}}: 	
(a + b) + c  =  a + (b + c)
(a * b) * c  =  a * (b * c)



The "Distributive Law" is the BEST one of all, but needs careful attention.

This is what it lets you do:

3*(2+4)

the 3* can be "distributed" across the 2+4, into 3*2 and 3*4



the "Distributive Law" says:

you get the same answer when you:

    multiply a number by a group of numbers added together, or
    do each multiply separately then add them



{{{Distributive}}} {{{Law}}}: 

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

These laws are to do with adding or multiplying, {{{not}}} dividing or subtracting.

The Commutative Law {{{does}}}{{{ not}}} work for division:

Example:

    12 / 3 = 4, but
    3 / 12 = ¼

The Associative Law {{{does}}}{{{ not}}} work for subtraction:

Example:

    (9 – 4) – 3 = 5 – 3 = 2, but
    9 – (4 – 3) = 9 – 1 = 8

 The Distributive Law {{{does}}}{{{ not}}} work for division:

Example:

    24 / (4 + 8) = 24 / 12 = 2, but
    24 / 4 + 24 / 8 = 6 + 3 = 9