Solution - Adding, subtracting and finding the least common multiple

Step  1  :

             81
 Simplify   ———
            100

Equation at the end of step  1  :

     4  60   3   81
  ((——+———)+——)+———
    10 100  10  100

Step  2  :

             3
 Simplify   ——
            10

Equation at the end of step  2  :

     4     60      3      81
  ((—— +  ———) +  ——) +  ———
    10    100     10     100

Step  3  :

            3
 Simplify   —
            5

Equation at the end of step  3  :

     4    3      3      81
  ((—— +  —) +  ——) +  ———
    10    5     10     100

Step  4  :

            2
 Simplify   —
            5

Equation at the end of step  4  :

    2    3      3      81
  ((— +  —) +  ——) +  ———
    5    5     10     100

Step  5  :

Adding fractions which have a common denominator :

 5.1       Adding fractions which 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 + 3     1
 —————  =  —
   5       1

Equation at the end of step  5  :

   1     3      81
  (— +  ——) +  ———
   1    10     100

Step  6  :

Rewriting the whole as an Equivalent Fraction :

 6.1   Adding a fraction to a whole

Rewrite the whole as a fraction using  10  as the denominator :

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

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 :

 6.2       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 + 3     13
 ——————  =  ——
   10       10

Equation at the end of step  6  :

  13     81
  —— +  ———
  10    100

Step  7  :

Calculating the Least Common Multiple :

 7.1    Find the Least Common Multiple

      The left denominator is :       10 

      The right denominator is :       100 

      Least Common Multiple:
      100 

Calculating Multipliers :

 7.2    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 = 10

   Right_M = L.C.M / R_Deno = 1

Making Equivalent Fractions :

 7.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      13 • 10
   ——————————————————  =   ———————
         L.C.M               100  

   R. Mult. • R. Num.       81
   ——————————————————  =   ———
         L.C.M             100

Adding fractions that have a common denominator :

 7.4       Adding up the two equivalent fractions

 13 • 10 + 81     211
 ————————————  =  ———
     100          100

Final result :

  211           
  ——— = 2.11000 
  100