Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "0.5" was replaced by "(5/10)". 3 more similar replacement(s)

Step  1  :

            1
 Simplify   —
            2

Equation at the end of step  1  :

   (3       2   1
  {——}2-(({——}3•—)
   10      10   2

Step  2  :

            1
 Simplify   —
            5

Equation at the end of step  2  :

   (3       1      1
  {——}2 - ((—)3) • —)
   10       5      2

Step  3  :

Equation at the end of step  3  :

    3       1   1
  {——}2 - (—— • —)
   10      53   2

Step  4  :

Equation at the end of step  4  :

    3      1 
  {——}2 - ———
   10     250

Step  5  :

             3
 Simplify   ——
            10

Equation at the end of step  5  :

    3        1 
  (——)2) -  ———
   10       250

Step  6  :

 6.1     10 = 2•5 (10)² = (2•5)² = 2² • 5²

Equation at the end of step  6  :

     32       1 
  ——————— -  ———
  (22•52)    250

Step  7  :

Calculating the Least Common Multiple :

 7.1    Find the Least Common Multiple

      The left denominator is :       100 

      The right denominator is :       250 

      Least Common Multiple:
      500 

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

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.      9 • 5
   ——————————————————  =   —————
         L.C.M              500 

   R. Mult. • R. Num.       2 
   ——————————————————  =   ———
         L.C.M             500

Adding fractions that have a common denominator :

 7.4       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:

 9 • 5 - (2)      43
 ———————————  =  ———
     500         500

Final result :

   43           
  ——— = 0.08600 
  500