Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "31.287" was replaced by "(31287/1000)". 3 more similar replacement(s)

Step  1  :

            31287
 Simplify   —————
            1000 

Equation at the end of step  1  :

   5325    131     31287
  (———— +  ———) +  —————
   100     10      1000 

Step  2  :

            131
 Simplify   ———
            10 

Equation at the end of step  2  :

   5325    131     31287
  (———— +  ———) +  —————
   100     10      1000 

Step  3  :

            213
 Simplify   ———
             4 

Equation at the end of step  3  :

   213    131     31287
  (——— +  ———) +  —————
    4     10      1000 

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       4 

      The right denominator is :       10 

      Least Common Multiple:
      20 

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 = 5

   Right_M = L.C.M / R_Deno = 2

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.      213 • 5
   ——————————————————  =   ———————
         L.C.M               20   

   R. Mult. • R. Num.      131 • 2
   ——————————————————  =   ———————
         L.C.M               20   

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:

 213 • 5 + 131 • 2     1327
 —————————————————  =  ————
        20              20 

Equation at the end of step  4  :

  1327    31287
  ———— +  —————
   20     1000 

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       20 

      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 = 50

   Right_M = L.C.M / R_Deno = 1

Making Equivalent Fractions :

 5.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      1327 • 50
   ——————————————————  =   —————————
         L.C.M               1000   

   R. Mult. • R. Num.      31287
   ——————————————————  =   —————
         L.C.M             1000 

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 1327 • 50 + 31287     97637
 —————————————————  =  —————
       1000            1000 

Final result :

  97637            
  ————— = 97.63700 
  1000