Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "0.1" was replaced by "(1/10)". 3 more similar replacement(s)

Step  1  :

             1
 Simplify   ——
            10

Equation at the end of step  1  :

         5678     943      1
  ((2 +  ————) +  ———) +  ——
         1000     100     10

Step  2  :

            943
 Simplify   ———
            100

Equation at the end of step  2  :

         5678     943      1
  ((2 +  ————) +  ———) +  ——
         1000     100     10

Step  3  :

            2839
 Simplify   ————
            500 

Equation at the end of step  3  :

         2839     943      1
  ((2 +  ————) +  ———) +  ——
         500      100     10

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Adding a fraction to a whole

Rewrite the whole as a fraction using  500  as the denominator :

          2     2 • 500
     2 =  —  =  ———————
          1       500  

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:

 2 • 500 + 2839     3839
 ——————————————  =  ————
      500           500 

Equation at the end of step  4  :

   3839    943      1
  (———— +  ———) +  ——
   500     100     10

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       500 

      The right denominator is :       100 

      Least Common Multiple:
      500 

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 = 5

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.      3839
   ——————————————————  =   ————
         L.C.M             500 

   R. Mult. • R. Num.      943 • 5
   ——————————————————  =   ———————
         L.C.M               500  

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 3839 + 943 • 5     4277
 ——————————————  =  ————
      500           250 

Equation at the end of step  5  :

  4277     1
  ———— +  ——
  250     10

Step  6  :

Calculating the Least Common Multiple :

 6.1    Find the Least Common Multiple

      The left denominator is :       250 

      The right denominator is :       10 

      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 = 1

   Right_M = L.C.M / R_Deno = 25

Making Equivalent Fractions :

 6.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      4277
   ——————————————————  =   ————
         L.C.M             250 

   R. Mult. • R. Num.       25
   ——————————————————  =   ———
         L.C.M             250

Adding fractions that have a common denominator :

 6.4       Adding up the two equivalent fractions

 4277 + 25     2151
 —————————  =  ————
    250        125 

Final result :

  2151            
  ———— = 17.20800 
  125