Solution - Adding, subtracting and finding the least common multiple

Step  1  :

            5
 Simplify   —
            6

Equation at the end of step  1  :

   5 3     -2 5
  (—+—) ÷ (——-—)
   8 4     3  6

Step  2  :

            -2
 Simplify   ——
            3 

Equation at the end of step  2  :

   5    3     -2    5
  (— +  —) ÷ (—— -  —)
   8    4     3     6

Step  3  :

Calculating the Least Common Multiple :

 3.1    Find the Least Common Multiple

      The left denominator is :       3 

      The right denominator is :       6 

      Least Common Multiple:
      6 

Calculating Multipliers :

 3.2    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 :

 3.3      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.      -2 • 2
   ——————————————————  =   ——————
         L.C.M               6   

   R. Mult. • R. Num.      5
   ——————————————————  =   —
         L.C.M             6

Adding fractions that have a common denominator :

 3.4       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:

 -2 • 2 - (5)     -3
 ————————————  =  ——
      6           2 

Equation at the end of step  3  :

   5    3    -3
  (— +  —) ÷ ——
   8    4    2 

Step  4  :

            3
 Simplify   —
            4

Equation at the end of step  4  :

   5    3    -3
  (— +  —) ÷ ——
   8    4    2 

Step  5  :

            5
 Simplify   —
            8

Equation at the end of step  5  :

   5    3    -3
  (— +  —) ÷ ——
   8    4    2 

Step  6  :

Calculating the Least Common Multiple :

 6.1    Find the Least Common Multiple

      The left denominator is :       8 

      The right denominator is :       4 

      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 = 1

   Right_M = L.C.M / R_Deno = 2

Making Equivalent Fractions :

 6.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      5
   ——————————————————  =   —
         L.C.M             8

   R. Mult. • R. Num.      3 • 2
   ——————————————————  =   —————
         L.C.M               8  

Adding fractions that have a common denominator :

 6.4       Adding up the two equivalent fractions

 5 + 3 • 2     11
 —————————  =  ——
     8         8 

Equation at the end of step  6  :

  11   -3
  —— ÷ ——
  8    2 

Step  7  :

         11      -3
 Divide  ——  by  ——
         8       2 

 7.1    Dividing fractions

To divide fractions, write the divison as multiplication by the reciprocal of the divisor :

11     -3       11      2
——  ÷  ——   =   ——  •  ——
8      2        8      -3

Final result :

   11            
  ——— = -0.91667 
  -12