Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "31.999" was replaced by "(31999/1000)". 3 more similar replacement(s)

Step  1  :

            31999
 Simplify   —————
            1000 

Equation at the end of step  1  :

   390983    35453     31999
  (—————— +  —————) +  —————
   10000     1000      1000 

Step  2  :

            35453
 Simplify   —————
            1000 

Equation at the end of step  2  :

   390983    35453     31999
  (—————— +  —————) +  —————
   10000     1000      1000 

Step  3  :

            390983
 Simplify   ——————
            10000 

Equation at the end of step  3  :

   390983    35453     31999
  (—————— +  —————) +  —————
   10000     1000      1000 

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       10000 

      The right denominator is :       1000 

      Least Common Multiple:
      10000 

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 = 1

   Right_M = L.C.M / R_Deno = 10

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.      390983
   ——————————————————  =   ——————
         L.C.M             10000 

   R. Mult. • R. Num.      35453 • 10
   ——————————————————  =   ——————————
         L.C.M               10000   

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:

 390983 + 35453 • 10     745513
 ———————————————————  =  ——————
        10000            10000 

Equation at the end of step  4  :

  745513    31999
  —————— +  —————
  10000     1000 

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       10000 

      The right denominator is :       1000 

      Least Common Multiple:
      10000 

Calculating Multipliers :

 5.2    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 = 1

   Right_M = L.C.M / R_Deno = 10

Making Equivalent Fractions :

 5.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      745513
   ——————————————————  =   ——————
         L.C.M             10000 

   R. Mult. • R. Num.      31999 • 10
   ——————————————————  =   ——————————
         L.C.M               10000   

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 745513 + 31999 • 10     1065503
 ———————————————————  =  ———————
        10000             10000 

Final result :

  1065503             
  ——————— = 106.55030 
   10000