Math properties?

Question

Please name all the properties that you know and how to use them for Algebra.
Please be specific and don't repeat what others say.

Thank you

Answer 1

a) Additive Identity of Zero (STANDARD)

Given any number, if you add zero to it, you get that number back. In
equations, for any number a, a + 0 = 0 + a = a.

b) Associative Property of Addition (STANDARD)

Given any three numbers to be added, the result of adding the sum of
the first and second to the third is the same as adding the first to
the sum of the second and third. In equations, for any three numbers
a, b, and c, (a + b) + c = a + (b + c).

c) Commutative Property of Addition (STANDARD)

Given any two numbers, the result of adding the first to the second
is the same as the result of adding the second to the first. In
equations, for any two numbers a and b, a + b = b + a.

d) Op-Op property (NON-STANDARD)

Given any number, the opposite of its opposite is the number itself.
In equations, for any number a, -(-a) = a.

e) Property of Opposites (NON-STANDARD)

Given any number, the sum of it and its opposite is zero. In
equations, for any number a, a + (-a) = 0

f) The associative property for addition merely states that:
a+(b+c) = (a+b)+c.

For multiplication, it would state that (ab)c = a(bc)

g) Commutative Property
An operation is commutative if you can change the order of the numbers involved without changing the result. Addition and multiplication are both commutative. Subtraction is not commutative: 2 - 1 is not equal to 1 - 2.

Here are some examples of the commutative properties of addition and multiplication:

88 + 65 = 65 + 88
153 = 153.

12 * 13 = 13 * 12
156 = 156.

More generally,

a + b = b + a, and
a * b = b * a.

There's also transitive, etc.

*If you are looking for some other ones just look up 'algebraic properties' into a search engine

Answer 2

1. commutative property 2. identity property of addition

Answer 3

commutative property a+b = b+a
associative property (a+b) + c = (a+c) + b
dfistributive property a(b+c) = ab + ac
identity propert a*1 = a
zero property a*0 = 0