Solution - Adding, subtracting and finding the least common multiple

Step  1  :

            31
 Simplify   ——
            11

Equation at the end of step  1  :

  48          31
  —— -  (0 -  ——)
  19          11

Step  2  :

            48
 Simplify   ——
            19

Equation at the end of step  2  :

  48    -31
  —— -  ———
  19    11 

Step  3  :

Calculating the Least Common Multiple :

 3.1    Find the Least Common Multiple

      The left denominator is :       19 

      The right denominator is :       11 

      Least Common Multiple:
      209 

Calculating Multipliers :

 3.2    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 = 11

   Right_M = L.C.M / R_Deno = 19

Making Equivalent Fractions :

 3.3      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.      48 • 11
   ——————————————————  =   ———————
         L.C.M               209  

   R. Mult. • R. Num.      -31 • 19
   ——————————————————  =   ————————
         L.C.M               209   

Adding fractions that have a common denominator :

 3.4       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:

 48 • 11 - (-31 • 19)     1117
 ————————————————————  =  ————
         209              209 

Final result :

  1117           
  ———— = 5.34450 
  209