Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "1.175" was replaced by "(1175/1000)".

Step  1  :

            47
 Simplify   ——
            40

Equation at the end of step  1  :

   115     1     47
  (——— +  ——) +  ——
   100    50     40

Step  2  :

             1
 Simplify   ——
            50

Equation at the end of step  2  :

   115     1     47
  (——— +  ——) +  ——
   100    50     40

Step  3  :

            23
 Simplify   ——
            20

Equation at the end of step  3  :

   23     1     47
  (—— +  ——) +  ——
   20    50     40

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       20 

      The right denominator is :       50 

      Least Common Multiple:
      100 

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 = 2

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.      23 • 5
   ——————————————————  =   ——————
         L.C.M              100  

   R. Mult. • R. Num.       2 
   ——————————————————  =   ———
         L.C.M             100

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:

 23 • 5 + 2     117
 ——————————  =  ———
    100         100

Equation at the end of step  4  :

  117    47
  ——— +  ——
  100    40

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       100 

      The right denominator is :       40 

      Least Common Multiple:
      200 

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 = 5

Making Equivalent Fractions :

 5.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      117 • 2
   ——————————————————  =   ———————
         L.C.M               200  

   R. Mult. • R. Num.      47 • 5
   ——————————————————  =   ——————
         L.C.M              200  

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 117 • 2 + 47 • 5     469
 ————————————————  =  ———
       200            200

Final result :

  469           
  ——— = 2.34500 
  200