Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-5" was replaced by "^(-5)".

(2): "22.55" was replaced by "(2255/100)".

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

  2255    
  ———— -  ((2)(-5)•(5)(-5))
  100     

Step  2  :

            451
 Simplify   ———
            20 

Equation at the end of step  2  :

  451    
  ——— -  ((2)(-5)•(5)(-5))
  20     

Step  3  :

 3.1      Finding a Common Denominator   The left  20 
 The right  25 • 55 

 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. 

 20 • 25 • 55   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 = 2⁵ • 5⁵

   Right_M = L.C.M / R_Deno = 20

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.     451 • (25•55)
   ——————————————————  =  —————————————
             Common denomi20 • (25•55) 

   R. Mult. • R. Num.                       20     
   ——————————————————  =               ————————————
             Common denominator        20 • (25•55)

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:

 451 • (25•55) - (20)     11•41•25•55 - 20
 ————————————————————  =  ————————————————
     20 • (25•55)           20 • (25•55)  

Final result :

    451 - 20  
  ————————————
  20 • (25•55)