Solution - Reducing fractions to their lowest terms

Step  1  :

            1
 Simplify   —
            2

Equation at the end of step  1  :

   1   4            1
  (—•(——•(-22)))-(2•—)
   2  23            2

Step  2  :

 2.1   Negative number raised to an even power is positive 

For example let's look at (-7)⁶ , where (-7) , a negative number, is raised to 6 , an even exponent :

(-7)⁶ can be written as (-7)•(-7)•(-7)•(-7)•(-7)•(-7)

Now, using the rule that says minus times minus is plus, (-7)⁶ can be written as (49)•(49)•(49) which in turn can be written as (7)•(7)•(7)•(7)•(7)•(7) or 7⁶ which is positive.

We proved that (-7)⁶ is equal to (7)⁶ which is a positive number

Using the same arguments as above, replacing (-7) by any negative number, and replacing the exponent 6 by any even exponent, we proved which had to be proved

Equation at the end of step  2  :

   1     4            
  (— • (—— • 22)) -  1
   2    23            

Step  3  :

             4
 Simplify   ——
            23

Equation at the end of step  3  :

   1     4            
  (— • (—— • 22)) -  1
   2    23            

Step  4  :

Multiplying exponents :

 4.1    2²  multiplied by  2²   = 2^{(2 + 2)} = 2⁴

Equation at the end of step  4  :

   1   16     
  (— • ——) -  1
   2   23     

Step  5  :

            1
 Simplify   —
            2

Equation at the end of step  5  :

   1   16     
  (— • ——) -  1
   2   23     

Step  6  :

Rewriting the whole as an Equivalent Fraction :

 6.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  23  as the denominator :

         1     1 • 23
    1 =  —  =  ——————
         1       23  

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 :

 6.2       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:

 8 - (23)     -15
 ————————  =  ———
    23        23 

Final result :

  -15            
  ——— = -0.65217 
  23