Solution - Adding, subtracting and finding the least common multiple

Step  1  :

            9
 Simplify   —
            4

Equation at the end of step  1  :

    49     2     9
  (——— -  ——) -  —
   144    12     4

Step  2  :

            1
 Simplify   —
            6

Equation at the end of step  2  :

    49    1     9
  (——— -  —) -  —
   144    6     4

Step  3  :

             49
 Simplify   ———
            144

Equation at the end of step  3  :

    49    1     9
  (——— -  —) -  —
   144    6     4

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       144 

      The right denominator is :       6 

      Least Common Multiple:
      144 

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 = 24

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.       49
   ——————————————————  =   ———
         L.C.M             144

   R. Mult. • R. Num.       24
   ——————————————————  =   ———
         L.C.M             144

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:

 49 - (24)      25
 —————————  =  ———
    144        144

Equation at the end of step  4  :

   25    9
  ——— -  —
  144    4

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       144 

      The right denominator is :       4 

      Least Common Multiple:
      144 

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 = 1

   Right_M = L.C.M / R_Deno = 36

Making Equivalent Fractions :

 5.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.       25
   ——————————————————  =   ———
         L.C.M             144

   R. Mult. • R. Num.      9 • 36
   ——————————————————  =   ——————
         L.C.M              144  

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 25 - (9 • 36)     -299
 —————————————  =  ————
      144          144 

Final result :

  -299            
  ———— = -2.07639 
  144