Question

I just need a description of the following:
Associative property of Multiplication
Associative Property of Addition
Commutative properties
Distributive Property
Identity property(I don't need to know much about this)
Zero property(i don't need to know much about this)

Answer 1

ADDITION:
associative a+(b+c) = (a+b) + c
commutative a+b = b+a
identity : there is a number 0 with
a+0=0+a = a
inverse a + -a = -a + a = 0

MULTIPLICATION:
associative a(bc) = (ab)c
commutative ab=ba
identity there is a number 1 with
a*1 = 1*a = a
inverse If a not zero then there is an 1/a such that a(1/a) = (1/a)a = 1

BOTH (the biggie!!)
distributive a(b+c) = ab + ac

Answer 2

Associative property of Multiplication:

(x*y)*z = x*(y*z)

Associative property of Addition:

(x + y) + z = x + (y + z)

Commutative properties:

x*y = y*x

x + y = y + x

Distributive Property :

x*(y + z) = x*y + x*z

Identity property: There exists a number 1 such that:

1*x = x for all x.

Zero property: There exists a number 0 such that:

0 + x = x for all x

Inverse properties:

For every x there exists a number -x, such that:

x + (-x) = 0

For every x not equal to zero there exists a number x^(-1), such that:

x*x^(-1) = 1


Examples:

There can only be one 0. Proof suppose there were two numbers 0 and 0' that both satisfy the property that the zero element has to satsify, then:

0 + 0' = 0'

because 0 is a zero element.

But because 0' is also a zero element, you also have:

0 + 0' = 0

This means that 0 = 0'


Example:

(-1)*x = -x

Proof:

Let's check of (-1)*x satisfies the criterium of being the inverse (relative to addition) of x:

x + (-1)*x =

1*x + (-1)*x =

(1 + (-1))*x = (use that -1 is the inverse relative to addition of 1)

0*x = 0

So, we can conclude that (-1)*x is the inverse of x relative to addition, which means that (-1)*x = -x

Answer 3

thank u soooooo much!

Answer 4

thank u soooooooooooooooo much, i really needed to understand this.