Solution - Adding, subtracting and finding the least common multiple

Step  1  :

            1
 Simplify   —
            4

Equation at the end of step  1  :

    3 1  1  1
  ((—+—)-—)+—
    8 8  3  4

Step  2  :

            1
 Simplify   —
            3

Equation at the end of step  2  :

    3    1     1     1
  ((— +  —) -  —) +  —
    8    8     3     4

Step  3  :

            1
 Simplify   —
            8

Equation at the end of step  3  :

    3    1     1     1
  ((— +  —) -  —) +  —
    8    8     3     4

Step  4  :

            3
 Simplify   —
            8

Equation at the end of step  4  :

    3    1     1     1
  ((— +  —) -  —) +  —
    8    8     3     4

Step  5  :

Adding fractions which have a common denominator :

 5.1       Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

 3 + 1     1
 —————  =  —
   8       2

Equation at the end of step  5  :

   1    1     1
  (— -  —) +  —
   2    3     4

Step  6  :

Calculating the Least Common Multiple :

 6.1    Find the Least Common Multiple

      The left denominator is :       2 

      The right denominator is :       3 

      Least Common Multiple:
      6 

Calculating Multipliers :

 6.2    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 = 2

Making Equivalent Fractions :

 6.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      3
   ——————————————————  =   —
         L.C.M             6

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

Adding fractions that have a common denominator :

 6.4       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:

 3 - (2)     1
 ———————  =  —
    6        6

Equation at the end of step  6  :

  1    1
  — +  —
  6    4

Step  7  :

Calculating the Least Common Multiple :

 7.1    Find the Least Common Multiple

      The left denominator is :       6 

      The right denominator is :       4 

      Least Common Multiple:
      12 

Calculating Multipliers :

 7.2    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 = 2

   Right_M = L.C.M / R_Deno = 3

Making Equivalent Fractions :

 7.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.       2
   ——————————————————  =   ——
         L.C.M             12

   R. Mult. • R. Num.       3
   ——————————————————  =   ——
         L.C.M             12

Adding fractions that have a common denominator :

 7.4       Adding up the two equivalent fractions

 2 + 3      5
 —————  =  ——
  12       12

Final result :

   5           
  —— = 0.41667 
  12