Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "5.01" was replaced by "(501/100)". 3 more similar replacement(s)

Step  1  :

            501
 Simplify   ———
            100

Equation at the end of step  1  :

         119     1737     501
  ((7 +  ———) +  ————) +  ———
         10      100      100

Step  2  :

            1737
 Simplify   ————
            100 

Equation at the end of step  2  :

         119     1737     501
  ((7 +  ———) +  ————) +  ———
         10      100      100

Step  3  :

            119
 Simplify   ———
            10 

Equation at the end of step  3  :

         119     1737     501
  ((7 +  ———) +  ————) +  ———
         10      100      100

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Adding a fraction to a whole

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

          7     7 • 10
     7 =  —  =  ——————
          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 :

 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:

 7 • 10 + 119     189
 ————————————  =  ———
      10          10 

Equation at the end of step  4  :

   189    1737     501
  (——— +  ————) +  ———
   10     100      100

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       10 

      The right denominator is :       100 

      Least Common Multiple:
      100 

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 = 10

   Right_M = L.C.M / R_Deno = 1

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.      189 • 10
   ——————————————————  =   ————————
         L.C.M               100   

   R. Mult. • R. Num.      1737
   ——————————————————  =   ————
         L.C.M             100 

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 189 • 10 + 1737     3627
 ———————————————  =  ————
       100           100 

Equation at the end of step  5  :

  3627    501
  ———— +  ———
  100     100

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:

 3627 + 501     1032
 ——————————  =  ————
    100          25 

Final result :

  1032            
  ———— = 41.28000 
   25