Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-7" was replaced by "^(-7)".

(2): "55.5" was replaced by "(555/10)".

Step  1  :

 1.1     10 = 2•5

(10)^-7 = (2•5)^(-7) = (2)^(-7) • (5)^(-7)

Equation at the end of step  1  :

  555    
  ——— -  ((2)(-7)•(5)(-7))
  10     

Step  2  :

            111
 Simplify   ———
             2 

Equation at the end of step  2  :

  111    
  ——— -  ((2)(-7)•(5)(-7))
   2     

Step  3  :

 3.1      Finding a Common Denominator   The left  2 
 The right  27 • 57 

 The product of any two denominators can be used
 as a common denominator. 

 Said product is not necessarily the least common 
 denominator.

 As a matter of fact, whenever the two denominators
have a common factor, their product will be bigger
 than the least common denominator. 

Anyway, the product is a fine common denominator and
 can perfectly be used for 
 calculating multipliers, as well as for generating
 equivalent fractions. 

 2 • 27 • 57   will be used as a common denominator.

Calculating Multipliers :

 3.2    Calculate multipliers for the two fractions


    Denote the Least Common Multiple by  L.C.M 
    Denote the Left Multiplier by  Left_M 
    Denote the Right Multiplier by  Right_M 
    Denote the Left Deniminator by  L_Deno 
    Denote the Right Multiplier by  R_Deno 

   Left_M = L.C.M / L_Deno = 2⁷ • 5⁷

   Right_M = L.C.M / R_Deno = 2

Making Equivalent Fractions :

 3.3      Rewrite the two fractions into equivalent fractions

Two fractions are called equivalent if they have the same numeric value.

For example :  1/2   and  2/4  are equivalent,  y/(y+1)²   and  (y²+y)/(y+1)³  are equivalent as well.

To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

   L. Mult. • L. Num.     111 • (27•57)
   ——————————————————  =  —————————————
             Common denomi 2 • (27•57) 

   R. Mult. • R. Num.                       2     
   ——————————————————  =               ———————————
             Common denominator        2 • (27•57)

Adding fractions that have a common denominator :

 3.4       Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

 111 • (27•57) - (2)     3•37•27•57 - 2
 ———————————————————  =  ——————————————
     2 • (27•57)          2 • (27•57)  

Final result :

    111 - 2  
  ———————————
  2 • (27•57)