Solution - Reducing fractions to their lowest terms

Step  1  :

 1.1     6 = 2•3

(6)¹ = (2•3)¹ = 2 • 3

Equation at the end of step  1  :

  (82)    (2•3)
  ———— -  —————
   9        2  

Step  2  :

            (2•3)
 Simplify   —————
              2  

Raising to a Power :

 2.1      Canceling out  2  as it appears on both sides of the fraction line

Equation at the end of step  2  :

  (82)    
  ———— -  3
   9      

Step  3  :

 3.1     8 = 23

(8)² = (2³)² = 2⁶

Equation at the end of step  3  :

  26    
  —— -  3
  9     

Step  4  :

            26
 Simplify   ——
            9 

Equation at the end of step  4  :

  64    
  —— -  3
  9     

Step  5  :

Rewriting the whole as an Equivalent Fraction :

 5.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  9  as the denominator :

         3     3 • 9
    3 =  —  =  —————
         1       9  

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 :

 5.2       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:

 64 - (3 • 9)     37
 ————————————  =  ——
      9           9 

Final result :

  37           
  —— = 4.11111 
  9