Solution - Adding, subtracting and finding the least common multiple

Step  1  :

            2
 Simplify   —
            5

Equation at the end of step  1  :

    5    1     2
  (—— +  —) -  —
   12    3     5

Step  2  :

            1
 Simplify   —
            3

Equation at the end of step  2  :

    5    1     2
  (—— +  —) -  —
   12    3     5

Step  3  :

             5
 Simplify   ——
            12

Equation at the end of step  3  :

    5    1     2
  (—— +  —) -  —
   12    3     5

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       12 

      The right denominator is :       3 

      Least Common Multiple:
      12 

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 = 1

   Right_M = L.C.M / R_Deno = 4

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.       5
   ——————————————————  =   ——
         L.C.M             12

   R. Mult. • R. Num.       4
   ——————————————————  =   ——
         L.C.M             12

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:

 5 + 4     3
 —————  =  —
  12       4

Equation at the end of step  4  :

  3    2
  — -  —
  4    5

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       4 

      The right denominator is :       5 

      Least Common Multiple:
      20 

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 = 4

Making Equivalent Fractions :

 5.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      3 • 5
   ——————————————————  =   —————
         L.C.M              20  

   R. Mult. • R. Num.      2 • 4
   ——————————————————  =   —————
         L.C.M              20  

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 3 • 5 - (2 • 4)      7
 ———————————————  =  ——
       20            20

Final result :

   7           
  —— = 0.35000 
  20