Associative, Commutative, and Distributive Properties are some simple rules for working with mathematical equations and expressions.
The associative property of addition and multiplication basically states when you are performing the same operation multiple times in a row, the order in which they are performed doesn't matter. You can group with parentheses anyway you want and it will not change the final value.
Examples:
Addition:
a+b+c = (a+b)+c = a+(b+c)
2+3+4 = (2+3)+4 = 2+(3+4) = 9
Multiplication:
abc = (ab)c = a(bc)
2*3*4 = (2*3)*4 = 2*(3*4) = 24
So as you can see the order that we performed the computations did not matter. To be clear you can not mix the operators up and still expect this to work. For example consider the following:
2*3+4 != 2(3+4)
In this case since the operators are not the same you can't place the parentheses anywhere you want. PEMDAS NEVAR 4 GET!
The commutative property of addition and multiplication says you can change the order around however you like and the final result will be the same. This does not mean you can perform the operations in any order you want, just that you can move stuff around...
Examples:
Addition:
a+b+c = b+a+c = c+b+a
2+3+4 = 3+2+4 = 4+3+2
Multiplication:
abc = bac = cab
2*3*4 = 3*2*4 = 4*2*3
Mixed: a+b+c*d = (d*c)+b+a
You can also you subtraction if you think of it like adding a negative
Example:
a+b-c = -c+a+b
1+2-3 = -3+2+1 = 0
The distributive property says that multiplication of real numbers distributes over addition or subtraction of real numbers.
Examples:
4(3+4) = (4*3) + (4*4) = 28
4(3-2) = (4*3) - (4*2) = 4
4(x+y) = 4x + 4y
4(x-y) = 4x - 4y
