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 :

                     5/12-n+5/4-(2/3)=0 

Step by step solution :

Step  1  :

            2
 Simplify   —
            3

Equation at the end of step  1  :

     5          5     2
  ((—— -  n) +  —) -  —  = 0 
    12          4     3

Step  2  :

            5
 Simplify   —
            4

Equation at the end of step  2  :

     5          5     2
  ((—— -  n) +  —) -  —  = 0 
    12          4     3

Step  3  :

             5
 Simplify   ——
            12

Equation at the end of step  3  :

     5          5     2
  ((—— -  n) +  —) -  —  = 0 
    12          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  12  as the denominator :

         n     n • 12
    n =  —  =  ——————
         1       12  

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:

 5 - (n • 12)     5 - 12n
 ————————————  =  ———————
      12            12   

Equation at the end of step  4  :

   (5 - 12n)    5     2
  (————————— +  —) -  —  = 0 
      12        4     3

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       12 

      The right denominator is :       4 

      Least Common Multiple:
      12 

Calculating Multipliers :

 5.2    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 = 1

   Right_M = L.C.M / R_Deno = 3

Making Equivalent Fractions :

 5.3      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.      (5-12n)
   ——————————————————  =   ———————
         L.C.M               12   

   R. Mult. • R. Num.      5 • 3
   ——————————————————  =   —————
         L.C.M              12  

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 (5-12n) + 5 • 3     20 - 12n
 ———————————————  =  ————————
       12               12   

Equation at the end of step  5  :

  (20 - 12n)    2
  —————————— -  —  = 0 
      12        3

Step  6  :

Step  7  :

Pulling out like terms :

 7.1     Pull out like factors :

   20 - 12n  =   -4 • (3n - 5) 

Adding fractions which have a common denominator :

 7.2       Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

 (5-3n) - (2)     3 - 3n
 ————————————  =  ——————
      3             3   

Step  8  :

Pulling out like terms :

 8.1     Pull out like factors :

   3 - 3n  =   -3 • (n - 1) 

Equation at the end of step  8  :

  1 - n  = 0 

Step  9  :

Solving a Single Variable Equation :

 9.1      Solve  :    -n+1 = 0 

 Subtract  1  from both sides of the equation : 
                      -n = -1
Multiply both sides of the equation by (-1) :  n = 1

One solution was found :