Solution - Adding, subtracting and finding the least common multiple

Step  1  :

            1
 Simplify   —
            4

Equation at the end of step  1  :

          8     3     1
  ((0 -  ——) -  —) -  —
         11     4     4

Step  2  :

            3
 Simplify   —
            4

Equation at the end of step  2  :

          8     3     1
  ((0 -  ——) -  —) -  —
         11     4     4

Step  3  :

             8
 Simplify   ——
            11

Equation at the end of step  3  :

          8     3     1
  ((0 -  ——) -  —) -  —
         11     4     4

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       11 

      The right denominator is :       4 

      Least Common Multiple:
      44 

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 = 4

   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.      -8 • 4
   ——————————————————  =   ——————
         L.C.M               44  

   R. Mult. • R. Num.      3 • 11
   ——————————————————  =   ——————
         L.C.M               44  

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:

 -8 • 4 - (3 • 11)     -65
 —————————————————  =  ———
        44             44 

Equation at the end of step  4  :

  -65    1
  ——— -  —
  44     4

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       44 

      The right denominator is :       4 

      Least Common Multiple:
      44 

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 = 11

Making Equivalent Fractions :

 5.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      -65
   ——————————————————  =   ———
         L.C.M             44 

   R. Mult. • R. Num.      11
   ——————————————————  =   ——
         L.C.M             44

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 -65 - (11)     -19
 ——————————  =  ———
     44         11 

Final result :

  -19            
  ——— = -1.72727 
  11