Solution - Adding, subtracting and finding the least common multiple

Step  1  :

             1 
 Simplify   ———
            121

Equation at the end of step  1  :

  6     1 
  — -  ——— ÷ 84
  7    121

Step  2  :

          1       
 Divide  ———  by  84
         121      

Equation at the end of step  2  :

  6      1  
  — -  —————
  7    10164

Step  3  :

            6
 Simplify   —
            7

Equation at the end of step  3  :

  6      1  
  — -  —————
  7    10164

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       7 

      The right denominator is :       10164 

      Least Common Multiple:
      10164 

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 = 1452

   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.      6 • 1452
   ——————————————————  =   ————————
         L.C.M              10164  

   R. Mult. • R. Num.        1  
   ——————————————————  =   —————
         L.C.M             10164

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:

 6 • 1452 - (1)      8711
 ——————————————  =  —————
     10164          10164

Final result :

   8711           
  ————— = 0.85704 
  10164