Solution - Adding, subtracting and finding the least common multiple

Step  1  :

            8
 Simplify   —
            1

Equation at the end of step  1  :

          5      6     
  ((0 -  ——) +  ——) +  8
         10     13     

Step  2  :

             6
 Simplify   ——
            13

Equation at the end of step  2  :

          5      6     
  ((0 -  ——) +  ——) +  8
         10     13     

Step  3  :

            1
 Simplify   —
            2

Equation at the end of step  3  :

         1      6     
  ((0 -  —) +  ——) +  8
         2     13     

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       2 

      The right denominator is :       13 

      Least Common Multiple:
      26 

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 = 13

   Right_M = L.C.M / R_Deno = 2

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.      -1 • 13
   ——————————————————  =   ———————
         L.C.M               26   

   R. Mult. • R. Num.      6 • 2
   ——————————————————  =   —————
         L.C.M              26  

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:

 -1 • 13 + 6 • 2     -1
 ———————————————  =  ——
       26            26

Equation at the end of step  4  :

  -1    
  —— +  8
  26    

Step  5  :

Rewriting the whole as an Equivalent Fraction :

 5.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  26  as the denominator :

         8     8 • 26
    8 =  —  =  ——————
         1       26  

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

 5.2       Adding up the two equivalent fractions

 -1 + 8 • 26     207
 ———————————  =  ———
     26          26 

Final result :

  207           
  ——— = 7.96154 
  26