Solution - Adding, subtracting and finding the least common multiple

Step  1  :

            4
 Simplify   —
            5

Equation at the end of step  1  :

   2    5     4
  (— +  —) -  —
   3    9     5

Step  2  :

            5
 Simplify   —
            9

Equation at the end of step  2  :

   2    5     4
  (— +  —) -  —
   3    9     5

Step  3  :

            2
 Simplify   —
            3

Equation at the end of step  3  :

   2    5     4
  (— +  —) -  —
   3    9     5

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       3 

      The right denominator is :       9 

      Least Common Multiple:
      9 

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 = 3

   Right_M = L.C.M / R_Deno = 1

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

   R. Mult. • R. Num.      5
   ——————————————————  =   —
         L.C.M             9

Adding fractions that have a common denominator :

 4.4       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:

 2 • 3 + 5     11
 —————————  =  ——
     9         9 

Equation at the end of step  4  :

  11    4
  —— -  —
  9     5

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       9 

      The right denominator is :       5 

      Least Common Multiple:
      45 

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 = 5

   Right_M = L.C.M / R_Deno = 9

Making Equivalent Fractions :

 5.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      11 • 5
   ——————————————————  =   ——————
         L.C.M               45  

   R. Mult. • R. Num.      4 • 9
   ——————————————————  =   —————
         L.C.M              45  

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 11 • 5 - (4 • 9)     19
 ————————————————  =  ——
        45            45

Final result :

  19           
  —— = 0.42222 
  45