Solution - Adding, subtracting and finding the least common multiple

Step  1  :

            35
 Simplify   ——
            48

Equation at the end of step  1  :

   65    25     35
  (—— +  ——) -  ——
   24    36     48

Step  2  :

            25
 Simplify   ——
            36

Equation at the end of step  2  :

   65    25     35
  (—— +  ——) -  ——
   24    36     48

Step  3  :

            65
 Simplify   ——
            24

Equation at the end of step  3  :

   65    25     35
  (—— +  ——) -  ——
   24    36     48

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       24 

      The right denominator is :       36 

      Least Common Multiple:
      72 

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 = 2

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.      65 • 3
   ——————————————————  =   ——————
         L.C.M               72  

   R. Mult. • R. Num.      25 • 2
   ——————————————————  =   ——————
         L.C.M               72  

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:

 65 • 3 + 25 • 2     245
 ———————————————  =  ———
       72            72 

Equation at the end of step  4  :

  245    35
  ——— -  ——
  72     48

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       72 

      The right denominator is :       48 

      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 = 2

   Right_M = L.C.M / R_Deno = 3

Making Equivalent Fractions :

 5.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      245 • 2
   ——————————————————  =   ———————
         L.C.M               144  

   R. Mult. • R. Num.      35 • 3
   ——————————————————  =   ——————
         L.C.M              144  

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 245 • 2 - (35 • 3)     385
 ——————————————————  =  ———
        144             144

Final result :

  385           
  ——— = 2.67361 
  144