Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "0.486" was replaced by "(486/1000)". 3 more similar replacement(s)

Step  1  :

            243
 Simplify   ———
            500

Equation at the end of step  1  :

    505    371     243     
  ((——— +  ———) +  ———) +  7
    100    10      500     

Step  2  :

            371
 Simplify   ———
            10 

Equation at the end of step  2  :

    505    371     243     
  ((——— +  ———) +  ———) +  7
    100    10      500     

Step  3  :

            101
 Simplify   ———
            20 

Equation at the end of step  3  :

    101    371     243     
  ((——— +  ———) +  ———) +  7
    20     10      500     

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       20 

      The right denominator is :       10 

      Least Common Multiple:
      20 

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 = 1

   Right_M = L.C.M / R_Deno = 2

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.      101
   ——————————————————  =   ———
         L.C.M             20 

   R. Mult. • R. Num.      371 • 2
   ——————————————————  =   ———————
         L.C.M               20   

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:

 101 + 371 • 2     843
 —————————————  =  ———
      20           20 

Equation at the end of step  4  :

   843    243     
  (——— +  ———) +  7
   20     500     

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       20 

      The right denominator is :       500 

      Least Common Multiple:
      500 

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 = 25

   Right_M = L.C.M / R_Deno = 1

Making Equivalent Fractions :

 5.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      843 • 25
   ——————————————————  =   ————————
         L.C.M               500   

   R. Mult. • R. Num.      243
   ——————————————————  =   ———
         L.C.M             500

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 843 • 25 + 243     10659
 ——————————————  =  —————
      500            250 

Equation at the end of step  5  :

  10659    
  ————— +  7
   250     

Step  6  :

Rewriting the whole as an Equivalent Fraction :

 6.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  250  as the denominator :

         7     7 • 250
    7 =  —  =  ———————
         1       250  

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 :

 6.2       Adding up the two equivalent fractions

 10659 + 7 • 250     12409
 ———————————————  =  —————
       250            250 

Final result :

  12409            
  ————— = 49.63600 
   250