Solution - Reducing fractions to their lowest terms

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "0.03" was replaced by "(03/100)".

Step  1  :

             3 
 Simplify   ———
            100

Equation at the end of step  1  :

                   03 
  ((f204) • a) -  (——— • g)
                   100

Step  2  :

                  3 
 Divide  40  by  ———
                 100

Equation at the end of step  2  :

                   4000
  ((f204) • a) -  (———— • g)
                    3  

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  3  as the denominator :

              f204a      f204a • 3 
     f204a =  —————  =  —————————
                1           3    

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 :

 3.2       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:

 f204a • 3 - (4000g)      3f204a - 4000g 
 ———————————————————  =  ——————————————
          3                    3       

Trying to factor as a Difference of Squares :

 3.3      Factoring:  3f²⁰⁴a - 4000g 

Theory : A difference of two perfect squares,  A² - B²  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =
         A² - AB + BA - B² =
         A² - AB + AB - B² =
         A² - B²

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check :  3  is not a square !!

Ruling : Binomial can not be factored as the
difference of two perfect squares

Trying to factor as a Difference of Cubes:

 3.4      Factoring:  3f²⁰⁴a - 4000g 

Theory : A difference of two perfect cubes,  a³ - b³ can be factored into
              (a-b) • (a² +ab +b²)

Proof :  (a-b)•(a²+ab+b²) =
            a³+a²b+ab²-ba²-b²a-b³ =
            a³+(a²b-ba²)+(ab²-b²a)-b³ =
            a³+0+0-b³ =
            a³-b³

Check :  3  is not a cube !!

Ruling : Binomial can not be factored as the difference of two perfect cubes

Final result :

  3f204a - 4000g 
  ——————————————
        3