Solution - Reducing fractions to their lowest terms

Step  1  :

 1.1   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

 1.2     74 = 2•37 (-74)² = (2•37)² = 2² • 37²

Equation at the end of step  1  :

   1                 
  (— • (22•372)) -  4
   3                 

Step  2  :

            1
 Simplify   —
            3

Equation at the end of step  2  :

   1                 
  (— • (22•372)) -  4
   3                 

Step  3  :

Equation at the end of step  3  :

  5476    
  ———— -  4
   3      

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  3  as the denominator :

         4     4 • 3
    4 =  —  =  —————
         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 :

 4.2       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:

 5476 - (4 • 3)     5464
 ——————————————  =  ————
       3             3  

Final result :

  5464              
  ———— = 1821.33333 
   3