All Properties of Math

Introduction to properties of math:

The mathematics is the arithmetic operations of addition, subtraction, multiplication, division, and algebra 1, the algebra is the branch of mathematics which deals with the rules of operations and relations, and the building and concepts occur from them, containing terms, polynomials. Algebra can be used with geometry, combinatorial, and number theory. Let us see all properties of mathematics

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All properties of mathematics:


All Reflexive Property

If somewhat is equal to its matching twin

X = X

All Symmetric Property

If somewhat turn over sides of the equivalent sign

X= y & y = x

All Transitive Property

If two objects are equal to a third object, the two are equal

X= y , z = y and x = z

All Commutative Property

If you inverted the order of addition or multiplication

X + y = y + x

All Associative Property

If you altered a alignment rearranged parenthesis, but kept the whole thing else in the same order

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

All Addition Property

If you added the similar non-zero numbers to equal sides

If x=y then

X + z = y + z

All Multiplication Property

If you multiplied the same nonzero number to both sides you have used this property

If x = y xz = yz

All Additive Identity

If you added 0 to get the same number back

X + 0 = x

All Multiplicative Identity

If you multiplied by 1 to get the same number back

(x)1 = x

All Property of Opposites

If you added opposite number’s and ended with 0

x + (-x) = 0

All Property of Reciprocals

If you multiplied by a reciprocal to get 1

(b)1/b=1.

All Distributive Property

If you multiplied x number into or pulled x number out of parenthesis

X ( y + z ) = xy + xz

Qr + rs = (q + s) r

All Multiplication Property of 0

If you multiplied by 0 and got 0

(a)0 = 0

All Multiplicative Property of (-1)

If you multiplied by (-1) and got the opposite of what you started with

X(-1) = -X

All Comparison Property

If you have stated that xy

All 1st Multiplication Property of Order

If you multiplied an inequality by a positive number and maintained the inequality

x < y, c is +, then xz < yz

All 2nd Multiplication Property of Order

If you multiplied as inequality by a negative number and reversed the inequality

x < y, c is –, then xz > yz

All Cancellation Property of Addition

If you cancelled the similar quantity from both sides of an equation (by subtracting)

x + y = y + z then x = y

All Cancellation Property of Multiplication

If you cancelled the same nonzero quantity from both sides of an equation (by division)

xz = yz so x = y

All Zero Product Property

If a product is zero, so you know that one of the factors has to be zero

xy = 0 if x = 0 or y = 0

All Definition of Division

If you changed a division to multiplication by a reciprocal

`x/y` = (x)1/y

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All Definition of Subtraction

If you have switched from adding a negative to just subtraction, or vice versa

x + (-y) = x - y

All Definition of Exponents

If you have also out of order apart exponents or shaped an exponent by multiplying a number by itself

(x) x = x2

All Substitution Property

If you have substitute one statement with an corresponding one and no other property or definition works