Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "9.85" was replaced by "(985/100)". 4 more similar replacement(s)

Step  1  :

            197
 Simplify   ———
            20 

Equation at the end of step  1  :

     1695 339      134  197
  (((————+———)+23)+———)+———
     100  10       10   20 

Step  2  :

            67
 Simplify   ——
            5 

Equation at the end of step  2  :

     1695 339      67  197
  (((————+———)+23)+——)+———
     100  10       5   20 

Step  3  :

            339
 Simplify   ———
            10 

Equation at the end of step  3  :

     1695    339            67     197
  (((———— +  ———) +  23) +  ——) +  ———
     100     10             5      20 

Step  4  :

            339
 Simplify   ———
            20 

Equation at the end of step  4  :

     339    339            67     197
  (((——— +  ———) +  23) +  ——) +  ———
     20     10             5      20 

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       20 

      The right denominator is :       10 

      Least Common Multiple:
      20 

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 = 1

   Right_M = L.C.M / R_Deno = 2

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.      339
   ——————————————————  =   ———
         L.C.M             20 

   R. Mult. • R. Num.      339 • 2
   ——————————————————  =   ———————
         L.C.M               20   

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:

 339 + 339 • 2     1017
 —————————————  =  ————
      20            20 

Equation at the end of step  5  :

    1017           67     197
  ((———— +  23) +  ——) +  ———
     20            5      20 

Step  6  :

Rewriting the whole as an Equivalent Fraction :

 6.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  20  as the denominator :

          23     23 • 20
    23 =  ——  =  ———————
          1        20   

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 :

 6.2       Adding up the two equivalent fractions

 1017 + 23 • 20     1477
 ——————————————  =  ————
       20            20 

Equation at the end of step  6  :

   1477    67     197
  (———— +  ——) +  ———
    20     5      20 

Step  7  :

Calculating the Least Common Multiple :

 7.1    Find the Least Common Multiple

      The left denominator is :       20 

      The right denominator is :       5 

      Least Common Multiple:
      20 

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 = 4

Making Equivalent Fractions :

 7.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      1477
   ——————————————————  =   ————
         L.C.M              20 

   R. Mult. • R. Num.      67 • 4
   ——————————————————  =   ——————
         L.C.M               20  

Adding fractions that have a common denominator :

 7.4       Adding up the two equivalent fractions

 1477 + 67 • 4     349
 —————————————  =  ———
      20            4 

Equation at the end of step  7  :

  349    197
  ——— +  ———
   4     20 

Step  8  :

Calculating the Least Common Multiple :

 8.1    Find the Least Common Multiple

      The left denominator is :       4 

      The right denominator is :       20 

      Least Common Multiple:
      20 

Calculating Multipliers :

 8.2    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 :

 8.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      349 • 5
   ——————————————————  =   ———————
         L.C.M               20   

   R. Mult. • R. Num.      197
   ——————————————————  =   ———
         L.C.M             20 

Adding fractions that have a common denominator :

 8.4       Adding up the two equivalent fractions

 349 • 5 + 197     971
 —————————————  =  ———
      20           10 

Final result :

  971            
  ——— = 97.10000 
  10