Solution - Adding, subtracting and finding the least common multiple

Step  1  :

              3 
 Simplify   ————
            1000

Equation at the end of step  1  :

    1     2        3 
  (—— +  ———) +  ————
   10    100     1000

Step  2  :

             1
 Simplify   ——
            50

Equation at the end of step  2  :

    1     1       3 
  (—— +  ——) +  ————
   10    50     1000

Step  3  :

             1
 Simplify   ——
            10

Equation at the end of step  3  :

    1     1       3 
  (—— +  ——) +  ————
   10    50     1000

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       10 

      The right denominator is :       50 

      Least Common Multiple:
      50 

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 = 1

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.       5
   ——————————————————  =   ——
         L.C.M             50

   R. Mult. • R. Num.       1
   ——————————————————  =   ——
         L.C.M             50

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:

 5 + 1      3
 —————  =  ——
  50       25

Equation at the end of step  4  :

   3      3 
  —— +  ————
  25    1000

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       25 

      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 = 40

   Right_M = L.C.M / R_Deno = 1

Making Equivalent Fractions :

 5.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      3 • 40
   ——————————————————  =   ——————
         L.C.M              1000 

   R. Mult. • R. Num.        3 
   ——————————————————  =   ————
         L.C.M             1000

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 3 • 40 + 3      123
 ——————————  =  ————
    1000        1000

Final result :

   123           
  ———— = 0.12300 
  1000