Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "10.9" was replaced by "(109/10)". 2 more similar replacement(s)

Step  1  :

            109
 Simplify   ———
            10 

Equation at the end of step  1  :

  823    109
  ——— +  ———
  100    10 

Step  2  :

            823
 Simplify   ———
            100

Equation at the end of step  2  :

  823    109
  ——— +  ———
  100    10 

Step  3  :

Calculating the Least Common Multiple :

 3.1    Find the Least Common Multiple

      The left denominator is :       100 

      The right denominator is :       10 

      Least Common Multiple:
      100 

Calculating Multipliers :

 3.2    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 = 10

Making Equivalent Fractions :

 3.3      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.      823
   ——————————————————  =   ———
         L.C.M             100

   R. Mult. • R. Num.      109 • 10
   ——————————————————  =   ————————
         L.C.M               100   

Adding fractions that have a common denominator :

 3.4       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:

 823 + 109 • 10     1913
 ——————————————  =  ————
      100           100 

Final result :

  1913            
  ———— = 19.13000 
  100