Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "0.005" was replaced by "(005/1000)". 3 more similar replacement(s)

Step  1  :

             1 
 Simplify   ———
            200

Equation at the end of step  1  :

   41      125       1 
  (—— -  ({———}2) ÷ ———
   10      100      200

Step  2  :

            5
 Simplify   —
            4

Equation at the end of step  2  :

   41     5        1 
  (—— -  (—)2)) ÷ ———
   10     4       200

Step  3  :

 3.1     4 = 2² (4)² = (2²)² = 2⁴

Equation at the end of step  3  :

   41    52     1 
  (—— -  ——) ÷ ———
   10    24    200

Step  4  :

            41
 Simplify   ——
            10

Equation at the end of step  4  :

   41    52     1 
  (—— -  ——) ÷ ———
   10    24    200

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       10 

      The right denominator is :       16 

      Least Common Multiple:
      80 

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 = 8

   Right_M = L.C.M / R_Deno = 5

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.      41 • 8
   ——————————————————  =   ——————
         L.C.M               80  

   R. Mult. • R. Num.      25 • 5
   ——————————————————  =   ——————
         L.C.M               80  

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:

 41 • 8 - (25 • 5)     203
 —————————————————  =  ———
        80             80 

Equation at the end of step  5  :

  203    1 
  ——— ÷ ———
  80    200

Step  6  :

         203       1 
 Divide  ———  by  ———
         80       200

 6.1    Dividing fractions

To divide fractions, write the divison as multiplication by the reciprocal of the divisor :

203      1        203     200
———  ÷  ———   =   ———  •  ———
80      200       80       1 

Final result :

  1015             
  ———— = 507.50000 
   2