Solution - Adding, subtracting and finding the least common multiple

Step  1  :

            5
 Simplify   —
            6

Equation at the end of step  1  :

       6     2   5
  ((0-——)+(0-—))-—
      11     3   6

Step  2  :

            2
 Simplify   —
            3

Equation at the end of step  2  :

          6           2      5
  ((0 -  ——) +  (0 -  —)) -  —
         11           3      6

Step  3  :

             6
 Simplify   ——
            11

Equation at the end of step  3  :

          6     -2     5
  ((0 -  ——) +  ——) -  —
         11     3      6

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       11 

      The right denominator is :       3 

      Least Common Multiple:
      33 

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 = 3

   Right_M = L.C.M / R_Deno = 11

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.      -6 • 3
   ——————————————————  =   ——————
         L.C.M               33  

   R. Mult. • R. Num.      -2 • 11
   ——————————————————  =   ———————
         L.C.M               33   

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:

 -6 • 3 + -2 • 11     -40
 ————————————————  =  ———
        33            33 

Equation at the end of step  4  :

  -40    5
  ——— -  —
  33     6

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       33 

      The right denominator is :       6 

      Least Common Multiple:
      66 

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 = 11

Making Equivalent Fractions :

 5.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      -40 • 2
   ——————————————————  =   ———————
         L.C.M               66   

   R. Mult. • R. Num.      5 • 11
   ——————————————————  =   ——————
         L.C.M               66  

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 -40 • 2 - (5 • 11)     -45
 ——————————————————  =  ———
         66             22 

Final result :

  -45            
  ——— = -2.04545 
  22