Solution - Adding, subtracting and finding the least common multiple

Step  1  :

            1
 Simplify   —
            2

Equation at the end of step  1  :

   3 1             1
  (—+— ÷ 1 ÷ 6)-(0-—)
   4 3             2

Step  2  :

            1
 Simplify   —
            3

Equation at the end of step  2  :

   3    1            -1
  (— +  — ÷ 1 ÷ 6) - ——
   4    3            2 

Step  3  :

         1      
 Divide  —  by  1
         3      

Equation at the end of step  3  :

   3    1         -1
  (— +  — ÷ 6) -  ——
   4    3         2 

Step  4  :

         1      
 Divide  —  by  6
         3      

Equation at the end of step  4  :

   3     1     -1
  (— +  ——) -  ——
   4    18     2 

Step  5  :

            3
 Simplify   —
            4

Equation at the end of step  5  :

   3     1     -1
  (— +  ——) -  ——
   4    18     2 

Step  6  :

Calculating the Least Common Multiple :

 6.1    Find the Least Common Multiple

      The left denominator is :       4 

      The right denominator is :       18 

      Least Common Multiple:
      36 

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 = 9

   Right_M = L.C.M / R_Deno = 2

Making Equivalent Fractions :

 6.3      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.      3 • 9
   ——————————————————  =   —————
         L.C.M              36  

   R. Mult. • R. Num.       2
   ——————————————————  =   ——
         L.C.M             36

Adding fractions that have a common denominator :

 6.4       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:

 3 • 9 + 2     29
 —————————  =  ——
    36         36

Equation at the end of step  6  :

  29    -1
  —— -  ——
  36    2 

Step  7  :

Calculating the Least Common Multiple :

 7.1    Find the Least Common Multiple

      The left denominator is :       36 

      The right denominator is :       2 

      Least Common Multiple:
      36 

Calculating Multipliers :

 7.2    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 = 18

Making Equivalent Fractions :

 7.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      29
   ——————————————————  =   ——
         L.C.M             36

   R. Mult. • R. Num.      -1 • 18
   ——————————————————  =   ———————
         L.C.M               36   

Adding fractions that have a common denominator :

 7.4       Adding up the two equivalent fractions

 29 - (-1 • 18)     47
 ——————————————  =  ——
       36           36

Final result :

  47           
  —— = 1.30556 
  36