Solution - Adding, subtracting and finding the least common multiple

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                     81/127-(x/16)=0 

Step by step solution :

Step  1  :

             x
 Simplify   ——
            16

Equation at the end of step  1  :

   81     x
  ——— -  ——  = 0 
  127    16

Step  2  :

             81
 Simplify   ———
            127

Equation at the end of step  2  :

   81     x
  ——— -  ——  = 0 
  127    16

Step  3  :

Calculating the Least Common Multiple :

 3.1    Find the Least Common Multiple

      The left denominator is :       127 

      The right denominator is :       16 

      Least Common Multiple:
      2032 

Calculating Multipliers :

 3.2    Calculate multipliers for the two fractions


    Denote the Least Common Multiple by  L.C.M 
    Denote the Left Multiplier by  Left_M 
    Denote the Right Multiplier by  Right_M 
    Denote the Left Deniminator by  L_Deno 
    Denote the Right Multiplier by  R_Deno 

   Left_M = L.C.M / L_Deno = 16

   Right_M = L.C.M / R_Deno = 127

Making Equivalent Fractions :

 3.3      Rewrite the two fractions into equivalent fractions

Two fractions are called equivalent if they have the same numeric value.

For example :  1/2   and  2/4  are equivalent,  y/(y+1)²   and  (y²+y)/(y+1)³  are equivalent as well.

To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

   L. Mult. • L. Num.      81 • 16
   ——————————————————  =   ———————
         L.C.M              2032  

   R. Mult. • R. Num.      x • 127
   ——————————————————  =   ———————
         L.C.M              2032  

Adding fractions that have a common denominator :

 3.4       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:

 81 • 16 - (x • 127)     1296 - 127x
 ———————————————————  =  ———————————
        2032                2032    

Equation at the end of step  3  :

  1296 - 127x
  ———————————  = 0 
     2032    

Step  4  :

When a fraction equals zero :

 4.1    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:

  1296-127x
  ————————— • 2032 = 0 • 2032
    2032   

Now, on the left hand side, the  2032  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
   1296-127x  = 0

Solving a Single Variable Equation :

 4.2      Solve  :    -127x+1296 = 0 

 Subtract  1296  from both sides of the equation : 
                      -127x = -1296
Multiply both sides of the equation by (-1) :  127x = 1296


Divide both sides of the equation by 127:
                     x = 1296/127 = 10.205

One solution was found :