Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "1.311" was replaced by "(1311/1000)". 3 more similar replacement(s)

Step  1  :

            1311
 Simplify   ————
            1000

Equation at the end of step  1  :

    75    226     1311     
  ((—— +  ———) +  ————) +  2
    10    100     1000     

Step  2  :

            113
 Simplify   ———
            50 

Equation at the end of step  2  :

    75    113     1311     
  ((—— +  ———) +  ————) +  2
    10    50      1000     

Step  3  :

            15
 Simplify   ——
            2 

Equation at the end of step  3  :

    15    113     1311     
  ((—— +  ———) +  ————) +  2
    2     50      1000     

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       2 

      The right denominator is :       50 

      Least Common Multiple:
      50 

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 = 25

   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.      15 • 25
   ——————————————————  =   ———————
         L.C.M               50   

   R. Mult. • R. Num.      113
   ——————————————————  =   ———
         L.C.M             50 

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:

 15 • 25 + 113     244
 —————————————  =  ———
      50           25 

Equation at the end of step  4  :

   244    1311     
  (——— +  ————) +  2
   25     1000     

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       25 

      The right denominator is :       1000 

      Least Common Multiple:
      1000 

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 = 40

   Right_M = L.C.M / R_Deno = 1

Making Equivalent Fractions :

 5.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      244 • 40
   ——————————————————  =   ————————
         L.C.M               1000  

   R. Mult. • R. Num.      1311
   ——————————————————  =   ————
         L.C.M             1000

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 244 • 40 + 1311     11071
 ———————————————  =  —————
      1000           1000 

Equation at the end of step  5  :

  11071    
  ————— +  2
  1000     

Step  6  :

Rewriting the whole as an Equivalent Fraction :

 6.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  1000  as the denominator :

         2     2 • 1000
    2 =  —  =  ————————
         1       1000  

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 :

 6.2       Adding up the two equivalent fractions

 11071 + 2 • 1000     13071
 ————————————————  =  —————
       1000           1000 

Final result :

  13071            
  ————— = 13.07100 
  1000