Solution - Reducing fractions to their lowest terms

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-3" was replaced by "^(-3)".

(2): "8.5" was replaced by "(85/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)^-3 = (2•5)^(-3) = (2)^(-3) • (5)^(-3)

Equation at the end of step  1  :

    5         85
  (——•(101))+(——•((2)(-3)•(5)(-3)))
   10         10

Step  2  :

            17
 Simplify   ——
            2 

Equation at the end of step  2  :

    5              17
  (—— • (101)) +  (—— • ((2)(-3)•(5)(-3)))
   10              2 

Step  3  :

Raising to a Power :

 3.1    2¹  multiplied by  2³   = 2^{(1 + 3)} = 2⁴

Equation at the end of step  3  :

    5              17 
  (—— • (101)) +  ————
   10             2000

Step  4  :

 4.1     10 = 2•5

(10)¹ = (2•5)¹ = 2 • 5

Equation at the end of step  4  :

    5              17 
  (—— • (2•5)) +  ————
   10             2000

Step  5  :

            1
 Simplify   —
            2

Equation at the end of step  5  :

   1              17 
  (— • (2•5)) +  ————
   2             2000

Step  6  :

Canceling Out :

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

Equation at the end of step  6  :

        17 
  5 +  ————
       2000

Step  7  :

Rewriting the whole as an Equivalent Fraction :

 7.1   Adding a fraction to a whole

Rewrite the whole as a fraction using  2000  as the denominator :

          5     5 • 2000
     5 =  —  =  ————————
          1       2000  

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 :

 7.2       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:

 5 • 2000 + 17     10017
 —————————————  =  —————
     2000          2000 

Final result :

  10017           
  ————— = 5.00850 
  2000