Solution - Adding, subtracting and finding the least common multiple

Step  1  :

            1
 Simplify   —
            3

Equation at the end of step  1  :

  5    1
  — +  — ÷ 6 ÷ 7
  6    3

Step  2  :

         1      
 Divide  —  by  6
         3      

Equation at the end of step  2  :

  5     1
  — +  —— ÷ 7
  6    18

Step  3  :

          1      
 Divide  ——  by  7
         18      

Equation at the end of step  3  :

  5     1 
  — +  ———
  6    126

Step  4  :

            5
 Simplify   —
            6

Equation at the end of step  4  :

  5     1 
  — +  ———
  6    126

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       6 

      The right denominator is :       126 

      Least Common Multiple:
      126 

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 = 21

   Right_M = L.C.M / R_Deno = 1

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 • 21
   ——————————————————  =   ——————
         L.C.M              126  

   R. Mult. • R. Num.       1 
   ——————————————————  =   ———
         L.C.M             126

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:

 5 • 21 + 1     53
 ——————————  =  ——
    126         63

Final result :

  53           
  —— = 0.84127 
  63