Solution - Adding, subtracting and finding the least common multiple

Step  1  :

             3
 Simplify   ——
            10

Equation at the end of step  1  :

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

Step  2  :

             1 
 Simplify   ———
            500

Equation at the end of step  2  :

    1      1       3
  (——— +  ———) +  ——
   100    500     10

Step  3  :

             1 
 Simplify   ———
            100

Equation at the end of step  3  :

    1      1       3
  (——— +  ———) +  ——
   100    500     10

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       100 

      The right denominator is :       500 

      Least Common Multiple:
      500 

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             500

   R. Mult. • R. Num.       1 
   ——————————————————  =   ———
         L.C.M             500

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 
 —————  =  ———
  500      250

Equation at the end of step  4  :

   3      3
  ——— +  ——
  250    10

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       250 

      The right denominator is :       10 

      Least Common Multiple:
      250 

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 = 25

Making Equivalent Fractions :

 5.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.       3 
   ——————————————————  =   ———
         L.C.M             250

   R. Mult. • R. Num.      3 • 25
   ——————————————————  =   ——————
         L.C.M              250  

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 3 + 3 • 25      39
 ——————————  =  ———
    250         125

Final result :

   39           
  ——— = 0.31200 
  125