Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "128.1281" was replaced by "(1281281/10000)". 3 more similar replacement(s)

Step  1  :

            1281281
 Simplify   ———————
             10000 

Equation at the end of step  1  :

    515           126     1281281
  ((——— +  10) +  ———) +  ———————
    100           10       10000 

Step  2  :

            63
 Simplify   ——
            5 

Equation at the end of step  2  :

    515           63     1281281
  ((——— +  10) +  ——) +  ———————
    100           5       10000 

Step  3  :

            103
 Simplify   ———
            20 

Equation at the end of step  3  :

    103           63     1281281
  ((——— +  10) +  ——) +  ———————
    20            5       10000 

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  20  as the denominator :

          10     10 • 20
    10 =  ——  =  ———————
          1        20   

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 :

 4.2       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:

 103 + 10 • 20     303
 —————————————  =  ———
      20           20 

Equation at the end of step  4  :

   303    63     1281281
  (——— +  ——) +  ———————
   20     5       10000 

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       20 

      The right denominator is :       5 

      Least Common Multiple:
      20 

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 = 4

Making Equivalent Fractions :

 5.3      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.      303
   ——————————————————  =   ———
         L.C.M             20 

   R. Mult. • R. Num.      63 • 4
   ——————————————————  =   ——————
         L.C.M               20  

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 303 + 63 • 4     111
 ————————————  =  ———
      20           4 

Equation at the end of step  5  :

  111    1281281
  ——— +  ———————
   4      10000 

Step  6  :

Calculating the Least Common Multiple :

 6.1    Find the Least Common Multiple

      The left denominator is :       4 

      The right denominator is :       10000 

      Least Common Multiple:
      10000 

Calculating Multipliers :

 6.2    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 = 2500

   Right_M = L.C.M / R_Deno = 1

Making Equivalent Fractions :

 6.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      111 • 2500
   ——————————————————  =   ——————————
         L.C.M               10000   

   R. Mult. • R. Num.      1281281
   ——————————————————  =   ———————
         L.C.M              10000 

Adding fractions that have a common denominator :

 6.4       Adding up the two equivalent fractions

 111 • 2500 + 1281281     1558781
 ————————————————————  =  ———————
        10000              10000 

Final result :

  1558781             
  ——————— = 155.87810 
   10000