Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "0.018" was replaced by "(018/1000)". 2 more similar replacement(s)

Step  1  :

             9 
 Simplify   ———
            500

Equation at the end of step  1  :

     75        9 
  ——————— -  (———)3)
  1000000     500

Step  2  :

 2.1     9 = 32

(9)³ = (3²)³ = 3⁶  2.2     500 = 2²•5³ (500)³ = (2²•5³)³ = 2⁶ • 5⁹

Equation at the end of step  2  :

     75         36  
  ——————— -  ———————
  1000000    (26•59)

Step  3  :

              3  
 Simplify   —————
            40000

Equation at the end of step  3  :

    3         36  
  ————— -  ———————
  40000    (26•59)

Step  4  :

 4.1      Finding a Common Denominator   The left  40000 
 The right  26 • 59 

 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. 

 40000 • 26 • 59   will be used as a common denominator.

Calculating Multipliers :

 4.2    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 = 2⁶ • 5⁹

   Right_M = L.C.M / R_Deno = 40000

Making Equivalent Fractions :

 4.3      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.                    3 • (26•59)  
   ——————————————————  =               ———————————————
             Common denominator        40000 • (26•59)

   R. Mult. • R. Num.                    729 • 40000  
   ——————————————————  =               ———————————————
             Common denominator        40000 • (26•59)

Adding fractions that have a common denominator :

 4.4       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:

 3 • (26•59) - (729 • 40000)     3•26•59 - 29160000
 ———————————————————————————  =  ——————————————————
       40000 • (26•59)            40000 • (26•59)  

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   3 • 2⁶ • 5⁹ - 29160000  =   3 • (1 - 9720000) 

Final result :

  3 • (1 + 9720000)
  —————————————————
   40000 • (26•59)