Solution - Reducing fractions to their lowest terms

Step  1  :

            2
 Simplify   —
            3

Equation at the end of step  1  :

           2
  (q2) -  (— • q)
           3
 Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Subtracting a fraction from a whole

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

           q2     q2 • 3
     q2 =  ——  =  ——————
           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 :

 2.2       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:

 q2 • 3 - (2q)     3q2 - 2q
 —————————————  =  ————————
       3              3    

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   3q² - 2q  =   q • (3q - 2) 

Final result :

  q • (3q + 2)
  ————————————
       3