Solution - Adding, subtracting and finding the least common multiple

Step  1  :

            9
 Simplify   —
            2

Equation at the end of step  1  :

        2     9
  (1 -  —) -  —
        3     2

Step  2  :

            2
 Simplify   —
            3

Equation at the end of step  2  :

        2     9
  (1 -  —) -  —
        3     2

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  3  as the denominator :

          1     1 • 3
     1 =  —  =  —————
          1       3  

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 :

 3.2       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:

 3 - (2)     1
 ———————  =  —
    3        3

Equation at the end of step  3  :

  1    9
  — -  —
  3    2

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       3 

      The right denominator is :       2 

      Least Common Multiple:
      6 

Calculating Multipliers :

 4.2    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 = 2

   Right_M = L.C.M / R_Deno = 3

Making Equivalent Fractions :

 4.3      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.      2
   ——————————————————  =   —
         L.C.M             6

   R. Mult. • R. Num.      9 • 3
   ——————————————————  =   —————
         L.C.M               6  

Adding fractions that have a common denominator :

 4.4       Adding up the two equivalent fractions

 2 - (9 • 3)     -25
 ———————————  =  ———
      6           6 

Final result :

  -25            
  ——— = -4.16667 
   6