Solution - Reducing fractions to their lowest terms

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "*-4" was replaced by "*(-4)".

(2): "10.5" was replaced by "(105/10)".

Step  1  :

            21
 Simplify   ——
            2 

Equation at the end of step  1  :

                 21
  (3 • (-42)) -  ——
                 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

 2.2     4 = 2² (-4)² = (2²)² = 2⁴

Equation at the end of step  2  :

              21
  (3 • 24) -  ——
              2 

Step  3  :

Equation at the end of step  3  :

            21
  (3•24) -  ——
            2 

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  2  as the denominator :

               (3•24)     (3•24) • 2
     (3•24) =  ——————  =  ——————————
                 1            2     

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:

 (3•24) • 2 - (21)     75
 —————————————————  =  ——
         2             2 

Final result :

  75            
  —— = 37.50000 
  2