Solution - Adding, subtracting and finding the least common multiple

Step  1  :

            2
 Simplify   —
            3

Equation at the end of step  1  :

       2          2
  (3 • —) -  (2 • —)
       5          3

Step  2  :

            2
 Simplify   —
            5

Equation at the end of step  2  :

       2     4
  (3 • —) -  —
       5     3

Step  3  :

Calculating the Least Common Multiple :

 3.1    Find the Least Common Multiple

      The left denominator is :       5 

      The right denominator is :       3 

      Least Common Multiple:
      15 

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 = 3

   Right_M = L.C.M / R_Deno = 5

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.      6 • 3
   ——————————————————  =   —————
         L.C.M              15  

   R. Mult. • R. Num.      4 • 5
   ——————————————————  =   —————
         L.C.M              15  

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:

 6 • 3 - (4 • 5)     -2
 ———————————————  =  ——
       15            15

Final result :

  -2            
  —— = -0.13333 
  15