Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "0.012" was replaced by "(012/1000)". 3 more similar replacement(s)

Step  1  :

             3 
 Simplify   ———
            250

Equation at the end of step  1  :

          12      12      3 
  ((12 +  ——) +  ———) +  ———
          10     100     250

Step  2  :

             3
 Simplify   ——
            25

Equation at the end of step  2  :

          12      3      3 
  ((12 +  ——) +  ——) +  ———
          10     25     250

Step  3  :

            6
 Simplify   —
            5

Equation at the end of step  3  :

          6      3      3 
  ((12 +  —) +  ——) +  ———
          5     25     250

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Adding a fraction to a whole

Rewrite the whole as a fraction using  5  as the denominator :

           12     12 • 5
     12 =  ——  =  ——————
           1        5   

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:

 12 • 5 + 6     66
 ——————————  =  ——
     5          5 

Equation at the end of step  4  :

   66     3      3 
  (—— +  ——) +  ———
   5     25     250

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       5 

      The right denominator is :       25 

      Least Common Multiple:
      25 

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 = 5

   Right_M = L.C.M / R_Deno = 1

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.      66 • 5
   ——————————————————  =   ——————
         L.C.M               25  

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

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 66 • 5 + 3     333
 ——————————  =  ———
     25         25 

Equation at the end of step  5  :

  333     3 
  ——— +  ———
  25     250

Step  6  :

Calculating the Least Common Multiple :

 6.1    Find the Least Common Multiple

      The left denominator is :       25 

      The right denominator is :       250 

      Least Common Multiple:
      250 

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 = 10

   Right_M = L.C.M / R_Deno = 1

Making Equivalent Fractions :

 6.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      333 • 10
   ——————————————————  =   ————————
         L.C.M               250   

   R. Mult. • R. Num.       3 
   ——————————————————  =   ———
         L.C.M             250

Adding fractions that have a common denominator :

 6.4       Adding up the two equivalent fractions

 333 • 10 + 3     3333
 ————————————  =  ————
     250          250 

Final result :

  3333            
  ———— = 13.33200 
  250