Solution - Adding, subtracting and finding the least common multiple

Step  1  :

             1
 Simplify   ——
            12

Equation at the end of step  1  :

           10     10      1
  ((100 +  ——) +  ——) +  ——
           3      4      12

Step  2  :

            5
 Simplify   —
            2

Equation at the end of step  2  :

           10     5      1
  ((100 +  ——) +  —) +  ——
           3      2     12

Step  3  :

            10
 Simplify   ——
            3 

Equation at the end of step  3  :

           10     5      1
  ((100 +  ——) +  —) +  ——
           3      2     12

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Adding a fraction to a whole

Rewrite the whole as a fraction using  3  as the denominator :

            100     100 • 3
     100 =  ———  =  ———————
             1         3   

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 :

 4.2       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:

 100 • 3 + 10     310
 ————————————  =  ———
      3            3 

Equation at the end of step  4  :

   310    5      1
  (——— +  —) +  ——
    3     2     12

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       3 

      The right denominator is :       2 

      Least Common Multiple:
      6 

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 = 2

   Right_M = L.C.M / R_Deno = 3

Making Equivalent Fractions :

 5.3      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.      310 • 2
   ——————————————————  =   ———————
         L.C.M                6   

   R. Mult. • R. Num.      5 • 3
   ——————————————————  =   —————
         L.C.M               6  

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 310 • 2 + 5 • 3     635
 ———————————————  =  ———
        6             6 

Equation at the end of step  5  :

  635     1
  ——— +  ——
   6     12

Step  6  :

Calculating the Least Common Multiple :

 6.1    Find the Least Common Multiple

      The left denominator is :       6 

      The right denominator is :       12 

      Least Common Multiple:
      12 

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 = 2

   Right_M = L.C.M / R_Deno = 1

Making Equivalent Fractions :

 6.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      635 • 2
   ——————————————————  =   ———————
         L.C.M               12   

   R. Mult. • R. Num.       1
   ——————————————————  =   ——
         L.C.M             12

Adding fractions that have a common denominator :

 6.4       Adding up the two equivalent fractions

 635 • 2 + 1     1271
 ———————————  =  ————
     12           12 

Final result :

  1271             
  ———— = 105.91667 
   12