Solution - Reducing fractions to their lowest terms

Step  1  :

            2
 Simplify   —
            3

Equation at the end of step  1  :

         1          2      
  ((2 -  —) • (3 -  —)) +  8
         2          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 :

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

 3 • 3 - (2)     7
 ———————————  =  —
      3          3

Equation at the end of step  2  :

         1    7     
  ((2 -  —) • —) +  8
         2    3     

Step  3  :

            1
 Simplify   —
            2

Equation at the end of step  3  :

         1    7     
  ((2 -  —) • —) +  8
         2    3     

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  2  as the denominator :

          2     2 • 2
     2 =  —  =  —————
          1       2  

Adding fractions that have a common denominator :

 4.2       Adding up the two equivalent fractions

 2 • 2 - (1)     3
 ———————————  =  —
      2          2

Equation at the end of step  4  :

   3   7     
  (— • —) +  8
   2   3     

Step  5  :

Rewriting the whole as an Equivalent Fraction :

 5.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  2  as the denominator :

         8     8 • 2
    8 =  —  =  —————
         1       2  

Adding fractions that have a common denominator :

 5.2       Adding up the two equivalent fractions

 7 + 8 • 2     23
 —————————  =  ——
     2         2 

Final result :

  23            
  —— = 11.50000 
  2