Solution - Reducing fractions to their lowest terms

Step  1  :

 1.1     4 = 22

(4)² = (2²)² = 2⁴

Equation at the end of step  1  :

   19
  {——}2 - 24
   -2

Step  2  :

            19
 Simplify   ——
            -2

Equation at the end of step  2  :

   19        
  (——)2) -  24
   -2        

Step  3  :

 3.1   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  3  :

  192    
  ——— -  24
  22     

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  2²  as the denominator :

          24     24 • 22
    24 =  ——  =  ———————
          1        22   

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:

 361 - (24 • 4)     297
 ——————————————  =  ———
       4             4 

Final result :

  297            
  ——— = 74.25000 
   4