Solution - Reducing fractions to their lowest terms

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "8.2" was replaced by "(82/10)".

Step  1  :

            41
 Simplify   ——
            5 

Equation at the end of step  1  :

         41     
  (10 +  ——) +  2
         5      

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Adding a fraction to a whole

Rewrite the whole as a fraction using  5  as the denominator :

           10     10 • 5
     10 =  ——  =  ——————
           1        5   

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:

 10 • 5 + 41     91
 ———————————  =  ——
      5          5 

Equation at the end of step  2  :

  91    
  —— +  2
  5     

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  5  as the denominator :

         2     2 • 5
    2 =  —  =  —————
         1       5  

Adding fractions that have a common denominator :

 3.2       Adding up the two equivalent fractions

 91 + 2 • 5     101
 ——————————  =  ———
     5           5 

Final result :

  101            
  ——— = 20.20000 
   5