Solution - Adding, subtracting and finding the least common multiple

Step  1  :

            1
 Simplify   —
            4

Equation at the end of step  1  :

    3 1  2  1
  ((—+—)-—)+—
    8 8  7  4

Step  2  :

            2
 Simplify   —
            7

Equation at the end of step  2  :

    3    1     2     1
  ((— +  —) -  —) +  —
    8    8     7     4

Step  3  :

            1
 Simplify   —
            8

Equation at the end of step  3  :

    3    1     2     1
  ((— +  —) -  —) +  —
    8    8     7     4

Step  4  :

            3
 Simplify   —
            8

Equation at the end of step  4  :

    3    1     2     1
  ((— +  —) -  —) +  —
    8    8     7     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    2     1
  (— -  —) +  —
   2    7     4

Step  6  :

Calculating the Least Common Multiple :

 6.1    Find the Least Common Multiple

      The left denominator is :       2 

      The right denominator is :       7 

      Least Common Multiple:
      14 

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 = 7

   Right_M = L.C.M / R_Deno = 2

Making Equivalent Fractions :

 6.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.       7
   ——————————————————  =   ——
         L.C.M             14

   R. Mult. • R. Num.      2 • 2
   ——————————————————  =   —————
         L.C.M              14  

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:

 7 - (2 • 2)      3
 ———————————  =  ——
     14          14

Equation at the end of step  6  :

   3    1
  —— +  —
  14    4

Step  7  :

Calculating the Least Common Multiple :

 7.1    Find the Least Common Multiple

      The left denominator is :       14 

      The right denominator is :       4 

      Least Common Multiple:
      28 

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 = 7

Making Equivalent Fractions :

 7.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      3 • 2
   ——————————————————  =   —————
         L.C.M              28  

   R. Mult. • R. Num.       7
   ——————————————————  =   ——
         L.C.M             28

Adding fractions that have a common denominator :

 7.4       Adding up the two equivalent fractions

 3 • 2 + 7     13
 —————————  =  ——
    28         28

Final result :

  13           
  —— = 0.46429 
  28