Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "45.5" was replaced by "(455/10)". 3 more similar replacement(s)

Step  1  :

            91
 Simplify   ——
            2 

Equation at the end of step  1  :

   677    6234     91
  (——— +  ————) +  ——
   10     100      2 

Step  2  :

            3117
 Simplify   ————
             50 

Equation at the end of step  2  :

   677    3117     91
  (——— +  ————) +  ——
   10      50      2 

Step  3  :

            677
 Simplify   ———
            10 

Equation at the end of step  3  :

   677    3117     91
  (——— +  ————) +  ——
   10      50      2 

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       10 

      The right denominator is :       50 

      Least Common Multiple:
      50 

Calculating Multipliers :

 4.2    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 = 1

Making Equivalent Fractions :

 4.3      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.      677 • 5
   ——————————————————  =   ———————
         L.C.M               50   

   R. Mult. • R. Num.      3117
   ——————————————————  =   ————
         L.C.M              50 

Adding fractions that have a common denominator :

 4.4       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:

 677 • 5 + 3117     3251
 ——————————————  =  ————
       50            25 

Equation at the end of step  4  :

  3251    91
  ———— +  ——
   25     2 

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       25 

      The right denominator is :       2 

      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 = 2

   Right_M = L.C.M / R_Deno = 25

Making Equivalent Fractions :

 5.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      3251 • 2
   ——————————————————  =   ————————
         L.C.M                50   

   R. Mult. • R. Num.      91 • 25
   ——————————————————  =   ———————
         L.C.M               50   

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 3251 • 2 + 91 • 25     8777
 ——————————————————  =  ————
         50              50 

Final result :

  8777             
  ———— = 175.54000 
   50