Solution - Adding, subtracting and finding the least common multiple

Step  1  :

            15
 Simplify   ——
            8 

Equation at the end of step  1  :

   11  3 20   15
  (——+(—•——))+——
   14  4 21   8 

Step  2  :

            20
 Simplify   ——
            21

Equation at the end of step  2  :

   11     3   20      15
  (—— +  (— • ——)) +  ——
   14     4   21      8 

Step  3  :

            3
 Simplify   —
            4

Equation at the end of step  3  :

   11     3   20      15
  (—— +  (— • ——)) +  ——
   14     4   21      8 

Step  4  :

            11
 Simplify   ——
            14

Equation at the end of step  4  :

   11    5     15
  (—— +  —) +  ——
   14    7     8 

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       14 

      The right denominator is :       7 

      Least Common Multiple:
      14 

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

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.      11
   ——————————————————  =   ——
         L.C.M             14

   R. Mult. • R. Num.      5 • 2
   ——————————————————  =   —————
         L.C.M              14  

Adding fractions that have a common denominator :

 5.4       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:

 11 + 5 • 2     3
 ——————————  =  —
     14         2

Equation at the end of step  5  :

  3    15
  — +  ——
  2    8 

Step  6  :

Calculating the Least Common Multiple :

 6.1    Find the Least Common Multiple

      The left denominator is :       2 

      The right denominator is :       8 

      Least Common Multiple:
      8 

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 = 4

   Right_M = L.C.M / R_Deno = 1

Making Equivalent Fractions :

 6.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      3 • 4
   ——————————————————  =   —————
         L.C.M               8  

   R. Mult. • R. Num.      15
   ——————————————————  =   ——
         L.C.M             8 

Adding fractions that have a common denominator :

 6.4       Adding up the two equivalent fractions

 3 • 4 + 15     27
 ——————————  =  ——
     8          8 

Final result :

  27           
  —— = 3.37500 
  8