Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "12.8" was replaced by "(128/10)". 4 more similar replacement(s)

Step  1  :

            64
 Simplify   ——
            5 

Equation at the end of step  1  :

    25 272   75  64
  ((——+———)+———)+——
    10 100  100  5 

Step  2  :

            3
 Simplify   —
            4

Equation at the end of step  2  :

    25    272     3     64
  ((—— +  ———) +  —) +  ——
    10    100     4     5 

Step  3  :

            68
 Simplify   ——
            25

Equation at the end of step  3  :

    25    68     3     64
  ((—— +  ——) +  —) +  ——
    10    25     4     5 

Step  4  :

            5
 Simplify   —
            2

Equation at the end of step  4  :

    5    68     3     64
  ((— +  ——) +  —) +  ——
    2    25     4     5 

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       2 

      The right denominator is :       25 

      Least Common Multiple:
      50 

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 = 25

   Right_M = L.C.M / R_Deno = 2

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.      5 • 25
   ——————————————————  =   ——————
         L.C.M               50  

   R. Mult. • R. Num.      68 • 2
   ——————————————————  =   ——————
         L.C.M               50  

Adding fractions that have a common denominator :

 5.4       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:

 5 • 25 + 68 • 2     261
 ———————————————  =  ———
       50            50 

Equation at the end of step  5  :

   261    3     64
  (——— +  —) +  ——
   50     4     5 

Step  6  :

Calculating the Least Common Multiple :

 6.1    Find the Least Common Multiple

      The left denominator is :       50 

      The right denominator is :       4 

      Least Common Multiple:
      100 

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 = 2

   Right_M = L.C.M / R_Deno = 25

Making Equivalent Fractions :

 6.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      261 • 2
   ——————————————————  =   ———————
         L.C.M               100  

   R. Mult. • R. Num.      3 • 25
   ——————————————————  =   ——————
         L.C.M              100  

Adding fractions that have a common denominator :

 6.4       Adding up the two equivalent fractions

 261 • 2 + 3 • 25     597
 ————————————————  =  ———
       100            100

Equation at the end of step  6  :

  597    64
  ——— +  ——
  100    5 

Step  7  :

Calculating the Least Common Multiple :

 7.1    Find the Least Common Multiple

      The left denominator is :       100 

      The right denominator is :       5 

      Least Common Multiple:
      100 

Calculating Multipliers :

 7.2    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 = 20

Making Equivalent Fractions :

 7.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      597
   ——————————————————  =   ———
         L.C.M             100

   R. Mult. • R. Num.      64 • 20
   ——————————————————  =   ———————
         L.C.M               100  

Adding fractions that have a common denominator :

 7.4       Adding up the two equivalent fractions

 597 + 64 • 20     1877
 —————————————  =  ————
      100          100 

Final result :

  1877            
  ———— = 18.77000 
  100