Solution - Adding, subtracting and finding the least common multiple

Step  1  :

            2
 Simplify   —
            3

Equation at the end of step  1  :

    2     1     2
  (—— +  ——) +  —
   11    17     3

Step  2  :

             1
 Simplify   ——
            17

Equation at the end of step  2  :

    2     1     2
  (—— +  ——) +  —
   11    17     3

Step  3  :

             2
 Simplify   ——
            11

Equation at the end of step  3  :

    2     1     2
  (—— +  ——) +  —
   11    17     3

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       11 

      The right denominator is :       17 

      Least Common Multiple:
      187 

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 = 17

   Right_M = L.C.M / R_Deno = 11

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.      2 • 17
   ——————————————————  =   ——————
         L.C.M              187  

   R. Mult. • R. Num.       11
   ——————————————————  =   ———
         L.C.M             187

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:

 2 • 17 + 11      45
 ———————————  =  ———
     187         187

Equation at the end of step  4  :

   45    2
  ——— +  —
  187    3

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       187 

      The right denominator is :       3 

      Least Common Multiple:
      561 

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 = 3

   Right_M = L.C.M / R_Deno = 187

Making Equivalent Fractions :

 5.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      45 • 3
   ——————————————————  =   ——————
         L.C.M              561  

   R. Mult. • R. Num.      2 • 187
   ——————————————————  =   ———————
         L.C.M               561  

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 45 • 3 + 2 • 187     509
 ————————————————  =  ———
       561            561

Final result :

  509           
  ——— = 0.90731 
  561