Solution - Reducing fractions to their lowest terms

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "10.1038" was replaced by "(101038/10000)".

Step  1  :

            50519
 Simplify   —————
            5000 

Equation at the end of step  1  :

    50519                              
  ((————— ÷ s41591 -  24) -  3217) -  5
    5000                               

Step  2  :

         50519      
 Divide  —————  by  s41591
         5000       

Equation at the end of step  2  :

     (72•1031)                    
  ((—————————— -  24) -  3217) -  5
    5000s41591                     

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  5000s⁴¹⁵⁹¹  as the denominator :

          24     24 • 5000s41591
    24 =  ——  =  ———————————————
          1        5000s41591   

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

 3.2       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:

 (72•1031) - (24 • 5000s41591)     72•1031 - 120000s41591
 —————————————————————————————  =  ——————————————————————
          5000s41591                     5000s41591      

Equation at the end of step  3  :

   (72•1031 - 120000s41591)             
  (———————————————————————— -  3217) -  5
          5000s41591                    

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  5000s⁴¹⁵⁹¹  as the denominator :

            3217     3217 • 5000s41591
    3217 =  ————  =  —————————————————
             1          5000s41591    

Adding fractions that have a common denominator :

 4.2       Adding up the two equivalent fractions

 (50519-120000s41591) - (3217 • 5000s41591)      50519 - 16205000s41591
 ——————————————————————————————————————————  =  ——————————————————————
                 5000s41591                           5000s41591      

Equation at the end of step  4  :

  (50519 - 16205000s41591)    
  ———————————————————————— -  5
         5000s41591           

Step  5  :

Rewriting the whole as an Equivalent Fraction :

 5.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  5000s⁴¹⁵⁹¹  as the denominator :

         5     5 • 5000s41591
    5 =  —  =  ——————————————
         1       5000s41591  

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   50519 - 16205000s⁴¹⁵⁹¹  =   7 • (7217 - 2315000s⁴¹⁵⁹¹) 

Adding fractions that have a common denominator :

 6.2       Adding up the two equivalent fractions

 7 • (7217-2315000s41591) - (5 • 5000s41591)      50519 - 16230000s41591
 ———————————————————————————————————————————  =  ——————————————————————
                 5000s41591                            5000s41591      

Final result :

  50519 - 16230000s41591
  ——————————————————————
        5000s41591