Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "31.75" was replaced by "(3175/100)". 3 more similar replacement(s)

Step  1  :

            127
 Simplify   ———
             4 

Equation at the end of step  1  :

          355     3925     127
  ((71 +  ———) +  ————) +  ———
          10      100       4 

Step  2  :

            157
 Simplify   ———
             4 

Equation at the end of step  2  :

          355     157     127
  ((71 +  ———) +  ———) +  ———
          10       4       4 

Step  3  :

            71
 Simplify   ——
            2 

Equation at the end of step  3  :

          71     157     127
  ((71 +  ——) +  ———) +  ———
          2       4       4 

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Adding a fraction to a whole

Rewrite the whole as a fraction using  2  as the denominator :

           71     71 • 2
     71 =  ——  =  ——————
           1        2   

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:

 71 • 2 + 71     213
 ———————————  =  ———
      2           2 

Equation at the end of step  4  :

   213    157     127
  (——— +  ———) +  ———
    2      4       4 

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       2 

      The right denominator is :       4 

      Least Common Multiple:
      4 

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 = 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.      213 • 2
   ——————————————————  =   ———————
         L.C.M                4   

   R. Mult. • R. Num.      157
   ——————————————————  =   ———
         L.C.M              4 

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 213 • 2 + 157     583
 —————————————  =  ———
       4            4 

Equation at the end of step  5  :

  583    127
  ——— +  ———
   4      4 

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:

 583 + 127     355
 —————————  =  ———
     4          2 

Final result :

  355             
  ——— = 177.50000 
   2