Solution - Adding, subtracting and finding the least common multiple

Step  1  :

            31
 Simplify   ——
            33

Equation at the end of step  1  :

     3  5  51  31
  ((——-——)+——)-——
    11 22  66  33

Step  2  :

            17
 Simplify   ——
            22

Equation at the end of step  2  :

     3     5     17     31
  ((—— -  ——) +  ——) -  ——
    11    22     22     33

Step  3  :

             5
 Simplify   ——
            22

Equation at the end of step  3  :

     3     5     17     31
  ((—— -  ——) +  ——) -  ——
    11    22     22     33

Step  4  :

             3
 Simplify   ——
            11

Equation at the end of step  4  :

     3     5     17     31
  ((—— -  ——) +  ——) -  ——
    11    22     22     33

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       11 

      The right denominator is :       22 

      Least Common Multiple:
      22 

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 = 2

   Right_M = L.C.M / R_Deno = 1

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.      3 • 2
   ——————————————————  =   —————
         L.C.M              22  

   R. Mult. • R. Num.       5
   ——————————————————  =   ——
         L.C.M             22

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:

 3 • 2 - (5)      1
 ———————————  =  ——
     22          22

Equation at the end of step  5  :

    1    17     31
  (—— +  ——) -  ——
   22    22     33

Step  6  :

Adding fractions which have a common denominator :

 6.1       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:

 1 + 17      9
 ——————  =  ——
   22       11

Equation at the end of step  6  :

   9    31
  —— -  ——
  11    33

Step  7  :

Calculating the Least Common Multiple :

 7.1    Find the Least Common Multiple

      The left denominator is :       11 

      The right denominator is :       33 

      Least Common Multiple:
      33 

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 = 3

   Right_M = L.C.M / R_Deno = 1

Making Equivalent Fractions :

 7.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      9 • 3
   ——————————————————  =   —————
         L.C.M              33  

   R. Mult. • R. Num.      31
   ——————————————————  =   ——
         L.C.M             33

Adding fractions that have a common denominator :

 7.4       Adding up the two equivalent fractions

 9 • 3 - (31)     -4
 ————————————  =  ——
      33          33

Final result :

  -4            
  —— = -0.12121 
  33