Solution - Adding, subtracting and finding the least common multiple

Step  1  :

            1
 Simplify   —
            6

Equation at the end of step  1  :

    5    7      1
  (——+(0-—))-(0-—)
   12    8      6

Step  2  :

            7
 Simplify   —
            8

Equation at the end of step  2  :

    5          7      -1
  (—— +  (0 -  —)) -  ——
   12          8      6 

Step  3  :

             5
 Simplify   ——
            12

Equation at the end of step  3  :

    5    -7     -1
  (—— +  ——) -  ——
   12    8      6 

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       12 

      The right denominator is :       8 

      Least Common Multiple:
      24 

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 = 2

   Right_M = L.C.M / R_Deno = 3

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.      5 • 2
   ——————————————————  =   —————
         L.C.M              24  

   R. Mult. • R. Num.      -7 • 3
   ——————————————————  =   ——————
         L.C.M               24  

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:

 5 • 2 + -7 • 3     -11
 ——————————————  =  ———
       24           24 

Equation at the end of step  4  :

  -11    -1
  ——— -  ——
  24     6 

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       24 

      The right denominator is :       6 

      Least Common Multiple:
      24 

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 = 4

Making Equivalent Fractions :

 5.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      -11
   ——————————————————  =   ———
         L.C.M             24 

   R. Mult. • R. Num.      -1 • 4
   ——————————————————  =   ——————
         L.C.M               24  

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 -11 - (-1 • 4)     -7
 ——————————————  =  ——
       24           24

Final result :

  -7            
  —— = -0.29167 
  24