Solution - Reducing fractions to their lowest terms

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "15.7" was replaced by "(157/10)".

Step  1  :

            157
 Simplify   ———
            10 

Equation at the end of step  1  :

      157                            
  ((((——— +  5) +  5) +  6) +  5) +  11
      10                             

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  10  as the denominator :

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

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:

 157 + 5 • 10     207
 ————————————  =  ———
      10          10 

Equation at the end of step  2  :

     207                      
  (((——— +  5) +  6) +  5) +  11
     10                       

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  10  as the denominator :

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

Adding fractions that have a common denominator :

 3.2       Adding up the two equivalent fractions

 207 + 5 • 10     257
 ————————————  =  ———
      10          10 

Equation at the end of step  3  :

    257                
  ((——— +  6) +  5) +  11
    10                 

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  10  as the denominator :

         6     6 • 10
    6 =  —  =  ——————
         1       10  

Adding fractions that have a common denominator :

 4.2       Adding up the two equivalent fractions

 257 + 6 • 10     317
 ————————————  =  ———
      10          10 

Equation at the end of step  4  :

   317          
  (——— +  5) +  11
   10           

Step  5  :

Rewriting the whole as an Equivalent Fraction :

 5.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  10  as the denominator :

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

Adding fractions that have a common denominator :

 5.2       Adding up the two equivalent fractions

 317 + 5 • 10     367
 ————————————  =  ———
      10          10 

Equation at the end of step  5  :

  367    
  ——— +  11
  10     

Step  6  :

Rewriting the whole as an Equivalent Fraction :

 6.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  10  as the denominator :

          11     11 • 10
    11 =  ——  =  ———————
          1        10   

Adding fractions that have a common denominator :

 6.2       Adding up the two equivalent fractions

 367 + 11 • 10     477
 —————————————  =  ———
      10           10 

Final result :

  477            
  ——— = 47.70000 
  10