Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "9.5" was replaced by "(95/10)". 4 more similar replacement(s)

Step  1  :

            19
 Simplify   ——
            2 

Equation at the end of step  1  :

     35  53    35   19
  ((———+————)+————)+——
    100 1000  1000  2 

Step  2  :

             7 
 Simplify   ———
            200

Equation at the end of step  2  :

     35     53       7      19
  ((——— +  ————) +  ———) +  ——
    100    1000     200     2 

Step  3  :

             53 
 Simplify   ————
            1000

Equation at the end of step  3  :

     35     53       7      19
  ((——— +  ————) +  ———) +  ——
    100    1000     200     2 

Step  4  :

             7
 Simplify   ——
            20

Equation at the end of step  4  :

     7     53       7      19
  ((—— +  ————) +  ———) +  ——
    20    1000     200     2 

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       20 

      The right denominator is :       1000 

      Least Common Multiple:
      1000 

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 = 50

   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.      7 • 50
   ——————————————————  =   ——————
         L.C.M              1000 

   R. Mult. • R. Num.       53 
   ——————————————————  =   ————
         L.C.M             1000

Adding fractions that have a common denominator :

 5.4       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:

 7 • 50 + 53      403
 ———————————  =  ————
    1000         1000

Equation at the end of step  5  :

    403     7      19
  (———— +  ———) +  ——
   1000    200     2 

Step  6  :

Calculating the Least Common Multiple :

 6.1    Find the Least Common Multiple

      The left denominator is :       1000 

      The right denominator is :       200 

      Least Common Multiple:
      1000 

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 = 1

   Right_M = L.C.M / R_Deno = 5

Making Equivalent Fractions :

 6.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.       403
   ——————————————————  =   ————
         L.C.M             1000

   R. Mult. • R. Num.      7 • 5
   ——————————————————  =   —————
         L.C.M             1000 

Adding fractions that have a common denominator :

 6.4       Adding up the two equivalent fractions

 403 + 7 • 5     219
 ———————————  =  ———
    1000         500

Equation at the end of step  6  :

  219    19
  ——— +  ——
  500    2 

Step  7  :

Calculating the Least Common Multiple :

 7.1    Find the Least Common Multiple

      The left denominator is :       500 

      The right denominator is :       2 

      Least Common Multiple:
      500 

Calculating Multipliers :

 7.2    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 = 250

Making Equivalent Fractions :

 7.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      219
   ——————————————————  =   ———
         L.C.M             500

   R. Mult. • R. Num.      19 • 250
   ——————————————————  =   ————————
         L.C.M               500   

Adding fractions that have a common denominator :

 7.4       Adding up the two equivalent fractions

 219 + 19 • 250     4969
 ——————————————  =  ————
      500           500 

Final result :

  4969           
  ———— = 9.93800 
  500