Solution - Adding, subtracting and finding the least common multiple

Step  1  :

            1
 Simplify   —
            3

Equation at the end of step  1  :

    6    4     1
  (—— +  —) +  —
   36    6     3

Step  2  :

            2
 Simplify   —
            3

Equation at the end of step  2  :

    6    2     1
  (—— +  —) +  —
   36    3     3

Step  3  :

            1
 Simplify   —
            6

Equation at the end of step  3  :

   1    2     1
  (— +  —) +  —
   6    3     3

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       6 

      The right denominator is :       3 

      Least Common Multiple:
      6 

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 = 1

   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.      1
   ——————————————————  =   —
         L.C.M             6

   R. Mult. • R. Num.      2 • 2
   ——————————————————  =   —————
         L.C.M               6  

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:

 1 + 2 • 2     5
 —————————  =  —
     6         6

Equation at the end of step  4  :

  5    1
  — +  —
  6    3

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       6 

      The right denominator is :       3 

      Least Common Multiple:
      6 

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 = 1

   Right_M = L.C.M / R_Deno = 2

Making Equivalent Fractions :

 5.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      5
   ——————————————————  =   —
         L.C.M             6

   R. Mult. • R. Num.      2
   ——————————————————  =   —
         L.C.M             6

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 5 + 2     7
 —————  =  —
   6       6

Final result :

  7           
  — = 1.16667 
  6