Rules for Elementary Algebra

Introduction to rules for elementary algebra:

Algebra is a system of written calculations that help us reason about numbers. At the very first, we should realize that algebra is a skill. The initial thing to note is that, in algebra, we use letters as well as numbers.  But the letters represent numbers.  And the rules of algebra match to the rules of arithmetic, but we write those rules using letters. Rules for elementary algebra is very basic in algebra, Now we are going to see about the rules for elementary algebra.

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Rules for elementary algebra part - I:


Property of zero

0 · x = 0
0 + x = x

Property of One

1 + x = 1
1. x = x

Identity Property

x · x = x
x + x = x

Redundancy Property

x · ( x + y ) = x
x + ( x · y ) = x

Commutative property

x · y = y · x
x + y = y + x

Associate Property

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

Distributive Property

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


Rules for elementary algebra part - II:


Properties of negation

a ( -1 ) = -a

-( -a ) = a

( -a ) b = - ( ab ) = a ( -b )

( -a ) ( -b ) = ab

-( a + b ) = ( -a ) + ( -b )

Properties of equality

If a + c = b + c, then a = b