Question 458473
Rule 1:

Addition of  two Numbers with the {{{same}}} sign

 The result is the {{{sum}}} of the numbers with the {{{given}}} sign ( the sign of the two numbers )  .

 When we add two  {{{plus}}} numbers we get a {{{plus}}} number.   Example :  {{{ 3+6=9}}}. 

 When we add two {{{minus}}} numbers we get a {{{minus}}} number.   Example:  {{{-5 + (- 6 )= - 11}}} .

Rule 2 :  

Addition of two numbers with {{{different}}} signs  the {{{result}}}is the {{{difference}}} between the numbers with the sign of the" {{{bigger}}}{{{ number}}} " .

  Example:   {{{6 + (- 9 )= - 3}}}

Rule 3 : 

Multiplication and signs :

  The basic rules for multiplication and signs  are as follows

{{{(Minus )( Minus ) =  Plus}}}    

{{{( Minus ) ( Plus )  = Minus}}}  

{{{(Plus ) (Plus )  =  Plus }}}


This can be expressed as follows that 

(a) when we multiply two  numbers with the same sign   we get {{{plus }}} 

 ( b) when we multiply  two numbers with difference signs  we get a {{{minus}}} 


Example : 

{{{ (- 7) * (- 5) =  35}}} 


{{{(-7 )* 5  = -35}}}  


Rule 4 :  Letters

Letters are often used in place of numbers , letters are often referred to  as {{{variables}}} or {{{unknowns}}} . 

Rules 1,2,3 above apply to all calculations with letters , we have to remember {{{one}}}{{{ further}}}{{{ rule}}} which applies to letters that is {{{we}}}{{{ can }}}{{{only }}}{{{add}}}{{{ things}}}{{{ together}}}{{{ that }}}{{{are }}}{{{the}}}{{{ same }}}, in other words we can only add x's to x's and y's to y's etc  .  


Example 

{{{5a - 7a = - 2a}}} ....Note also {{{5a }}}means {{{5}}} times{{{a }}}.

or

{{{ - 3x +  7x  = 4x}}}}

or

{{{ 5a + 6b - 4a - 11b ,= 5a - 4a  + 6b - 11b =  a - 5b }}}

Rule 5 :    Brackets 

(a) A number immediately outside a bracket means that everything inside the bracket gets multiplied by that number   

Ex.: {{{4(5)=4*5=20}}}

(b)Minus sign  outside a bracket will change all the signs inside the brackets when the brackets are removed : 

Ex.: {{{-4(5)=-4*5=-20}}}

(c)Minus number outside a bracket does two things 

(1) everything inside the bracket gets multiplied by the number and 

(2) all the signs change


{{{-(2x-3x)=-2x+3x=x}}}


Brackets by brackets :

Multiply everything in the second bracket by everything in the first bracket and tidy it up .

Ex.:  {{{(x-1)(x+1)=x^2+x-x+1*(-1)=x^2-1}}}