Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "21.05" was replaced by "(2105/100)". 2 more similar replacement(s)

Step  1  :

            421
 Simplify   ———
            20 

Equation at the end of step  1  :

    84916    421             
  ((————— +  ———) +  131) +  46
    1000     20              

Step  2  :

            21229
 Simplify   —————
             250 

Equation at the end of step  2  :

    21229    421             
  ((————— +  ———) +  131) +  46
     250     20              

Step  3  :

Calculating the Least Common Multiple :

 3.1    Find the Least Common Multiple

      The left denominator is :       250 

      The right denominator is :       20 

      Least Common Multiple:
      500 

Calculating Multipliers :

 3.2    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 = 2

   Right_M = L.C.M / R_Deno = 25

Making Equivalent Fractions :

 3.3      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.      21229 • 2
   ——————————————————  =   —————————
         L.C.M                500   

   R. Mult. • R. Num.      421 • 25
   ——————————————————  =   ————————
         L.C.M               500   

Adding fractions that have a common denominator :

 3.4       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:

 21229 • 2 + 421 • 25     52983
 ————————————————————  =  —————
         500               500 

Equation at the end of step  3  :

   52983            
  (————— +  131) +  46
    500             

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  500  as the denominator :

           131     131 • 500
    131 =  ———  =  —————————
            1         500   

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

 52983 + 131 • 500     118483
 —————————————————  =  ——————
        500             500  

Equation at the end of step  4  :

  118483    
  —————— +  46
   500      

Step  5  :

Rewriting the whole as an Equivalent Fraction :

 5.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  500  as the denominator :

          46     46 • 500
    46 =  ——  =  ————————
          1        500   

Adding fractions that have a common denominator :

 5.2       Adding up the two equivalent fractions

 118483 + 46 • 500     141483
 —————————————————  =  ——————
        500             500  

Final result :

  141483             
  —————— = 282.96600 
   500