Solution - Adding, subtracting and finding the least common multiple

Step  1  :

             2
 Simplify   ——
            71

Equation at the end of step  1  :

   3        2
  —— ÷ 8 - —— ÷ 4
  81       71

Step  2  :

          2      
 Divide  ——  by  4
         71      

Equation at the end of step  2  :

   3        1 
  —— ÷ 8 - ———
  81       142

Step  3  :

             1
 Simplify   ——
            27

Equation at the end of step  3  :

   1         1 
  —— ÷ 8 -  ———
  27        142

Step  4  :

          1      
 Divide  ——  by  8
         27      

Equation at the end of step  4  :

   1      1 
  ——— -  ———
  216    142

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       216 

      The right denominator is :       142 

      Least Common Multiple:
      15336 

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 = 71

   Right_M = L.C.M / R_Deno = 108

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.        71 
   ——————————————————  =   —————
         L.C.M             15336

   R. Mult. • R. Num.       108 
   ——————————————————  =   —————
         L.C.M             15336

Adding fractions that have a common denominator :

 5.4       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:

 71 - (108)      -37 
 ——————————  =  —————
   15336        15336

Final result :

   -37             
  ————— = -0.00241 
  15336