Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "0.096" was replaced by "(096/1000)". 4 more similar replacement(s)

Step  1  :

             12
 Simplify   ———
            125

Equation at the end of step  1  :

    15  6   24   12
  ((——+——)+———)+———
    10 10  100  125

Step  2  :

             6
 Simplify   ——
            25

Equation at the end of step  2  :

    15     6      6      12
  ((—— +  ——) +  ——) +  ———
    10    10     25     125

Step  3  :

            3
 Simplify   —
            5

Equation at the end of step  3  :

    15    3      6      12
  ((—— +  —) +  ——) +  ———
    10    5     25     125

Step  4  :

            3
 Simplify   —
            2

Equation at the end of step  4  :

    3    3      6      12
  ((— +  —) +  ——) +  ———
    2    5     25     125

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       2 

      The right denominator is :       5 

      Least Common Multiple:
      10 

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 = 5

   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.      3 • 5
   ——————————————————  =   —————
         L.C.M              10  

   R. Mult. • R. Num.      3 • 2
   ——————————————————  =   —————
         L.C.M              10  

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:

 3 • 5 + 3 • 2     21
 —————————————  =  ——
      10           10

Equation at the end of step  5  :

   21     6      12
  (—— +  ——) +  ———
   10    25     125

Step  6  :

Calculating the Least Common Multiple :

 6.1    Find the Least Common Multiple

      The left denominator is :       10 

      The right denominator is :       25 

      Least Common Multiple:
      50 

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 = 5

   Right_M = L.C.M / R_Deno = 2

Making Equivalent Fractions :

 6.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      21 • 5
   ——————————————————  =   ——————
         L.C.M               50  

   R. Mult. • R. Num.      6 • 2
   ——————————————————  =   —————
         L.C.M              50  

Adding fractions that have a common denominator :

 6.4       Adding up the two equivalent fractions

 21 • 5 + 6 • 2     117
 ——————————————  =  ———
       50           50 

Equation at the end of step  6  :

  117     12
  ——— +  ———
  50     125

Step  7  :

Calculating the Least Common Multiple :

 7.1    Find the Least Common Multiple

      The left denominator is :       50 

      The right denominator is :       125 

      Least Common Multiple:
      250 

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 = 5

   Right_M = L.C.M / R_Deno = 2

Making Equivalent Fractions :

 7.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      117 • 5
   ——————————————————  =   ———————
         L.C.M               250  

   R. Mult. • R. Num.      12 • 2
   ——————————————————  =   ——————
         L.C.M              250  

Adding fractions that have a common denominator :

 7.4       Adding up the two equivalent fractions

 117 • 5 + 12 • 2     609
 ————————————————  =  ———
       250            250

Final result :

  609           
  ——— = 2.43600 
  250