Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "0.3" was replaced by "(3/10)". 4 more similar replacement(s)

Step  1  :

             3
 Simplify   ——
            10

Equation at the end of step  1  :

     55 36  21      3
  (((——+——)+——)+1)+——
     10 10  10     10

Step  2  :

            21
 Simplify   ——
            10

Equation at the end of step  2  :

     55 36  21      3
  (((——+——)+——)+1)+——
     10 10  10     10

Step  3  :

            18
 Simplify   ——
            5 

Equation at the end of step  3  :

     55    18     21            3
  (((—— +  ——) +  ——) +  1) +  ——
     10    5      10           10

Step  4  :

            11
 Simplify   ——
            2 

Equation at the end of step  4  :

     11    18     21            3
  (((—— +  ——) +  ——) +  1) +  ——
     2     5      10           10

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       2 

      The right denominator is :       5 

      Least Common Multiple:
      10 

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 = 5

   Right_M = L.C.M / R_Deno = 2

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.      11 • 5
   ——————————————————  =   ——————
         L.C.M               10  

   R. Mult. • R. Num.      18 • 2
   ——————————————————  =   ——————
         L.C.M               10  

Adding fractions that have a common denominator :

 5.4       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:

 11 • 5 + 18 • 2     91
 ———————————————  =  ——
       10            10

Equation at the end of step  5  :

    91    21            3
  ((—— +  ——) +  1) +  ——
    10    10           10

Step  6  :

Adding fractions which have a common denominator :

 6.1       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:

 91 + 21     56
 ———————  =  ——
   10        5 

Equation at the end of step  6  :

   56           3
  (—— +  1) +  ——
   5           10

Step  7  :

Rewriting the whole as an Equivalent Fraction :

 7.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  5  as the denominator :

         1     1 • 5
    1 =  —  =  —————
         1       5  

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 :

 7.2       Adding up the two equivalent fractions

 56 + 5     61
 ——————  =  ——
   5        5 

Equation at the end of step  7  :

  61     3
  —— +  ——
  5     10

Step  8  :

Calculating the Least Common Multiple :

 8.1    Find the Least Common Multiple

      The left denominator is :       5 

      The right denominator is :       10 

      Least Common Multiple:
      10 

Calculating Multipliers :

 8.2    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 :

 8.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      61 • 2
   ——————————————————  =   ——————
         L.C.M               10  

   R. Mult. • R. Num.       3
   ——————————————————  =   ——
         L.C.M             10

Adding fractions that have a common denominator :

 8.4       Adding up the two equivalent fractions

 61 • 2 + 3     25
 ——————————  =  ——
     10         2 

Final result :

  25            
  —— = 12.50000 
  2