Solution - Adding, subtracting and finding the least common multiple

Step  1  :

             7
 Simplify   ——
            12

Equation at the end of step  1  :

          12      7     
  ((10 -  ——) +  ——) +  11
          8      12     

Step  2  :

            3
 Simplify   —
            2

Equation at the end of step  2  :

          3      7     
  ((10 -  —) +  ——) +  11
          2     12     

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  2  as the denominator :

           10     10 • 2
     10 =  ——  =  ——————
           1        2   

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 :

 3.2       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:

 10 • 2 - (3)     17
 ————————————  =  ——
      2           2 

Equation at the end of step  3  :

   17     7     
  (—— +  ——) +  11
   2     12     

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       2 

      The right denominator is :       12 

      Least Common Multiple:
      12 

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 = 6

   Right_M = L.C.M / R_Deno = 1

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.      17 • 6
   ——————————————————  =   ——————
         L.C.M               12  

   R. Mult. • R. Num.       7
   ——————————————————  =   ——
         L.C.M             12

Adding fractions that have a common denominator :

 4.4       Adding up the two equivalent fractions

 17 • 6 + 7     109
 ——————————  =  ———
     12         12 

Equation at the end of step  4  :

  109    
  ——— +  11
  12     

Step  5  :

Rewriting the whole as an Equivalent Fraction :

 5.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  12  as the denominator :

          11     11 • 12
    11 =  ——  =  ———————
          1        12   

Adding fractions that have a common denominator :

 5.2       Adding up the two equivalent fractions

 109 + 11 • 12     241
 —————————————  =  ———
      12           12 

Final result :

  241            
  ——— = 20.08333 
  12