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*d+1/6*d+1/3*d+1/12*d-(6)=0 

Step by step solution :

Step  1  :

             1
 Simplify   ——
            12

Equation at the end of step  1  :

       5     1      1       1
  ((((——•d)+(—•d))+(—•d))+(——•d))-6  = 0 
      12     6      3      12

Step  2  :

            1
 Simplify   —
            3

Equation at the end of step  2  :

       5     1      1      d
  ((((——•d)+(—•d))+(—•d))+——)-6  = 0 
      12     6      3     12

Step  3  :

            1
 Simplify   —
            6

Equation at the end of step  3  :

       5     1     d   d
  ((((——•d)+(—•d))+—)+——)-6  = 0 
      12     6     3  12

Step  4  :

             5
 Simplify   ——
            12

Equation at the end of step  4  :

       5         d     d      d     
  ((((—— • d) +  —) +  —) +  ——) -  6  = 0 
      12         6     3     12     

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       12 

      The right denominator is :       6 

      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 = 2

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.      5d
   ——————————————————  =   ——
         L.C.M             12

   R. Mult. • R. Num.      d • 2
   ——————————————————  =   —————
         L.C.M              12  

Adding fractions that have a common denominator :

 5.4       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:

 5d + d • 2     7d
 ——————————  =  ——
     12         12

Equation at the end of step  5  :

    7d    d      d     
  ((—— +  —) +  ——) -  6  = 0 
    12    3     12     

Step  6  :

Calculating the Least Common Multiple :

 6.1    Find the Least Common Multiple

      The left denominator is :       12 

      The right denominator is :       3 

      Least Common Multiple:
      12 

Calculating Multipliers :

 6.2    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 = 4

Making Equivalent Fractions :

 6.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      7d
   ——————————————————  =   ——
         L.C.M             12

   R. Mult. • R. Num.      d • 4
   ——————————————————  =   —————
         L.C.M              12  

Adding fractions that have a common denominator :

 6.4       Adding up the two equivalent fractions

 7d + d • 4     11d
 ——————————  =  ———
     12         12 

Equation at the end of step  6  :

   11d     d     
  (——— +  ——) -  6  = 0 
   12     12     

Step  7  :

Adding fractions which have a common denominator :

 7.1       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:

 11d + d     12d
 ———————  =  ———
   12        12 

Reducing to Lowest Terms :

 7.2      The above result can still be reduced :

     12d     
     ——— = d 
     12      

Equation at the end of step  7  :

  d -  6  = 0 

Step  8  :

Equation at the end of step  8  :

  d - 6  = 0 

Step  9  :

Solving a Single Variable Equation :

 9.1      Solve  :    d-6 = 0 

 Add  6  to both sides of the equation : 
                      d = 6

One solution was found :