Solution - Adding, subtracting and finding the least common multiple

Step  1  :

            4
 Simplify   —
            5

Equation at the end of step  1  :

    8    19     4
  (—— +  ——) -  —
   15    30     5

Step  2  :

            19
 Simplify   ——
            30

Equation at the end of step  2  :

    8    19     4
  (—— +  ——) -  —
   15    30     5

Step  3  :

             8
 Simplify   ——
            15

Equation at the end of step  3  :

    8    19     4
  (—— +  ——) -  —
   15    30     5

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       15 

      The right denominator is :       30 

      Least Common Multiple:
      30 

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 = 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.      8 • 2
   ——————————————————  =   —————
         L.C.M              30  

   R. Mult. • R. Num.      19
   ——————————————————  =   ——
         L.C.M             30

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:

 8 • 2 + 19     7
 ——————————  =  —
     30         6

Equation at the end of step  4  :

  7    4
  — -  —
  6    5

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       6 

      The right denominator is :       5 

      Least Common Multiple:
      30 

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 = 6

Making Equivalent Fractions :

 5.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      7 • 5
   ——————————————————  =   —————
         L.C.M              30  

   R. Mult. • R. Num.      4 • 6
   ——————————————————  =   —————
         L.C.M              30  

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 7 • 5 - (4 • 6)     11
 ———————————————  =  ——
       30            30

Final result :

  11           
  —— = 0.36667 
  30