a) The Additive Identity: any number added to zero will always equal itself

b) Multiplicative Inverse (Reciprocal): any number multiplied by its inverse (reciprocal) will always equal 1

c) Associative Property: Changing the grouping of numbers being added will not change its value. (note: this property is also True for multiplication, but not subtraction or division)

d) The Zero property of Multiplication: any number multiplied by zero will alway equal zero

Follow this website….it will give you the answers you are looking for and it also provides examples.

http://www.wtamu.edu/academic/anns/mps/math/mathlab/beg_algebra/beg_alg_tut8_property.htm

the first and foremost rule is order of operations. It dictates and controls every piece of math from arithmetic to number theory. It takes priority over all other operations. parenthesis, exponents multiplication/division, addition/subtraction. proceeding from left to right its important to note that multiplication and division are the same operation, and addition/subtraction are the same operation. I will give examples that will hopefuly demonstrate this .5 =1/2 so .5x =x/2 good so far? x/2=(1/2)x=1/2x. one divided by two times x. order of operations makes this so. it is NOT 1/(2x). You see this mistake very frequently. x+y=y+x it may seem obvious, but its a very important principle xy=yx it does not mater order you multiply x/2 is not the same as 2/x,but .5x=x(.5) so we have seen that x/2=(1/2)x (1/2)x=x(1/2) so far all should be easy the inverse of 2 is 1/2 when you divide x by two, you are actualy multiplying by its inverse. become comfortable with the idea that 1/2x=(1/2)x=x/2=.5x now consider x+y=y+x x-y=x+(-y) x-y=-y+x the take home point is that division and subtraction are really multiplication and addition. when you subract y from x, you are actualy adding a negative y to x now consider some algebra 5-(3x+5) this would be more properly expressed as 5+(-1)(3x+5) notice the unspoken -1 that actualy exists in the original expression. When I was first learning algebra, I always rewrote exresssion this way to clarify them. I still do it at times with calculus to this day. Never feel ashamed for symplifying stuff this far, and always use your calculator for simple arithmatic. 5+(-1)(3x+5) There is nothing inside the parenthesis that can be simplified any further. next you multiply. distribute the -1 over the parenthises 5+(-3x+(-5)) now addition, combine like terms 5+(-5)+(-3x)=-3x 10x/2y(3/x) one step at a time 1) 10 times x = 10x 2)10x divided by 2 =5x 3) 5x times y =5xy 4) 5xy divided by 3 = (5xy)/3 or (5/3)(xy) 5) (5/3)(xy) divided by x is (5/3)(xy)/x the x’s cancel so (5/3)(y) 5/3y=(5y)/3 one last important concept, x=(1)x^1/1 so 5 =5/1=(1)5=5^1 by extension -5=(-1)5 so -5(3x+2)=5(-3x-2) I could go on for a long time. I spend most of my tutoring time reinforcing these rules since most people troubles come from not focusing on the fundamental basics. It does not help that most grade school teachers have an education focused on education rather than math, and often do not understand the rules well, or simply have them wrong.

A) The Additive Property of Identity

B) The Multiplicative Property of Recipricals or Inverses

C) The Symmetric Property of Equality

D) The Multiplicative Property of Zero.

a) Additive identity property

b) Substitution property of equality

c) Associative property of addition

d) Multiplicative property of zero

Hope this helps!

– Elizabeth –