Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "14.27" was replaced by "(1427/100)". 3 more similar replacement(s)

Step  1  :

            1427
 Simplify   ————
            100 

Equation at the end of step  1  :

    822          197     1427
  ((——— +  3) +  ———) +  ————
    100          10      100 

Step  2  :

            197
 Simplify   ———
            10 

Equation at the end of step  2  :

    822          197     1427
  ((——— +  3) +  ———) +  ————
    100          10      100 

Step  3  :

            411
 Simplify   ———
            50 

Equation at the end of step  3  :

    411          197     1427
  ((——— +  3) +  ———) +  ————
    50           10      100 

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  50  as the denominator :

         3     3 • 50
    3 =  —  =  ——————
         1       50  

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:

 411 + 3 • 50     561
 ————————————  =  ———
      50          50 

Equation at the end of step  4  :

   561    197     1427
  (——— +  ———) +  ————
   50     10      100 

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       50 

      The right denominator is :       10 

      Least Common Multiple:
      50 

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 = 1

   Right_M = L.C.M / R_Deno = 5

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.      561
   ——————————————————  =   ———
         L.C.M             50 

   R. Mult. • R. Num.      197 • 5
   ——————————————————  =   ———————
         L.C.M               50   

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 561 + 197 • 5     773
 —————————————  =  ———
      50           25 

Equation at the end of step  5  :

  773    1427
  ——— +  ————
  25     100 

Step  6  :

Calculating the Least Common Multiple :

 6.1    Find the Least Common Multiple

      The left denominator is :       25 

      The right denominator is :       100 

      Least Common Multiple:
      100 

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 = 4

   Right_M = L.C.M / R_Deno = 1

Making Equivalent Fractions :

 6.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      773 • 4
   ——————————————————  =   ———————
         L.C.M               100  

   R. Mult. • R. Num.      1427
   ——————————————————  =   ————
         L.C.M             100 

Adding fractions that have a common denominator :

 6.4       Adding up the two equivalent fractions

 773 • 4 + 1427     4519
 ——————————————  =  ————
      100           100 

Final result :

  4519            
  ———— = 45.19000 
  100