Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "9.42" was replaced by "(942/100)". 3 more similar replacement(s)

Step  1  :

            471
 Simplify   ———
            50 

Equation at the end of step  1  :

    2    930905     471
  (—— +  ——————) +  ———
   10    100000     50 

Step  2  :

            186181
 Simplify   ——————
            20000 

Equation at the end of step  2  :

    2    186181     471
  (—— +  ——————) +  ———
   10    20000      50 

Step  3  :

            1
 Simplify   —
            5

Equation at the end of step  3  :

   1    186181     471
  (— +  ——————) +  ———
   5    20000      50 

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       5 

      The right denominator is :       20000 

      Least Common Multiple:
      20000 

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 = 4000

   Right_M = L.C.M / R_Deno = 1

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.       4000
   ——————————————————  =   —————
         L.C.M             20000

   R. Mult. • R. Num.      186181
   ——————————————————  =   ——————
         L.C.M             20000 

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:

 4000 + 186181     190181
 —————————————  =  ——————
     20000         20000 

Equation at the end of step  4  :

  190181    471
  —————— +  ———
  20000     50 

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       20000 

      The right denominator is :       50 

      Least Common Multiple:
      20000 

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 = 400

Making Equivalent Fractions :

 5.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      190181
   ——————————————————  =   ——————
         L.C.M             20000 

   R. Mult. • R. Num.      471 • 400
   ——————————————————  =   —————————
         L.C.M               20000  

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 190181 + 471 • 400     378581
 ——————————————————  =  ——————
       20000            20000 

Final result :

  378581            
  —————— = 18.92905 
  20000