Solution - Reducing fractions to their lowest terms

Reformatting the input :

Changes made to your input should not affect the solution:

(1): ".222" was replaced by "(222/1000)".

Step by step solution :

Step  1  :

            111
 Simplify   ———
            500

Equation at the end of step  1  :

       111     
  (r • ———) -  13  = 0 
       500     

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  500  as the denominator :

          13     13 • 500
    13 =  ——  =  ————————
          1        500   

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 :

 2.2       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:

 111r - (13 • 500)     111r - 6500
 —————————————————  =  ———————————
        500                500    

Equation at the end of step  2  :

  111r - 6500
  ———————————  = 0 
      500    

Step  3  :

When a fraction equals zero :

 3.1    When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

  111r-6500
  ————————— • 500 = 0 • 500
     500   

Now, on the left hand side, the  500  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
   111r-6500  = 0

Solving a Single Variable Equation :

 3.2      Solve  :    111r-6500 = 0 

 Add  6500  to both sides of the equation : 
                      111r = 6500
Divide both sides of the equation by 111:
                     r = 6500/111 = 58.559

One solution was found :