Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "1.23" was replaced by "(123/100)". 3 more similar replacement(s)

Step  1  :

            123
 Simplify   ———
            100

Equation at the end of step  1  :

     861          115     123
  ((———— +  1) +  ———) +  ———
    1000          100     100

Step  2  :

            23
 Simplify   ——
            20

Equation at the end of step  2  :

     861          23     123
  ((———— +  1) +  ——) +  ———
    1000          20     100

Step  3  :

             861
 Simplify   ————
            1000

Equation at the end of step  3  :

     861          23     123
  ((———— +  1) +  ——) +  ———
    1000          20     100

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  1000  as the denominator :

         1     1 • 1000
    1 =  —  =  ————————
         1       1000  

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 :

 4.2       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:

 861 + 1000     1861
 ——————————  =  ————
    1000        1000

Equation at the end of step  4  :

   1861    23     123
  (———— +  ——) +  ———
   1000    20     100

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       1000 

      The right denominator is :       20 

      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 = 1

   Right_M = L.C.M / R_Deno = 50

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.      1861
   ——————————————————  =   ————
         L.C.M             1000

   R. Mult. • R. Num.      23 • 50
   ——————————————————  =   ———————
         L.C.M              1000  

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 1861 + 23 • 50     3011
 ——————————————  =  ————
      1000          1000

Equation at the end of step  5  :

  3011    123
  ———— +  ———
  1000    100

Step  6  :

Calculating the Least Common Multiple :

 6.1    Find the Least Common Multiple

      The left denominator is :       1000 

      The right denominator is :       100 

      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 = 10

Making Equivalent Fractions :

 6.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      3011
   ——————————————————  =   ————
         L.C.M             1000

   R. Mult. • R. Num.      123 • 10
   ——————————————————  =   ————————
         L.C.M               1000  

Adding fractions that have a common denominator :

 6.4       Adding up the two equivalent fractions

 3011 + 123 • 10     4241
 ———————————————  =  ————
      1000           1000

Final result :

  4241           
  ———— = 4.24100 
  1000