Solution - Adding, subtracting and finding the least common multiple

Step  1  :

            915
 Simplify   ———
            16 

Equation at the end of step  1  :

   53    45     915
  (—— +  ——) +  ———
   15    16     16 

Step  2  :

            45
 Simplify   ——
            16

Equation at the end of step  2  :

   53    45     915
  (—— +  ——) +  ———
   15    16     16 

Step  3  :

            53
 Simplify   ——
            15

Equation at the end of step  3  :

   53    45     915
  (—— +  ——) +  ———
   15    16     16 

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       15 

      The right denominator is :       16 

      Least Common Multiple:
      240 

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 = 16

   Right_M = L.C.M / R_Deno = 15

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.      53 • 16
   ——————————————————  =   ———————
         L.C.M               240  

   R. Mult. • R. Num.      45 • 15
   ——————————————————  =   ———————
         L.C.M               240  

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:

 53 • 16 + 45 • 15     1523
 —————————————————  =  ————
        240            240 

Equation at the end of step  4  :

  1523    915
  ———— +  ———
  240     16 

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       240 

      The right denominator is :       16 

      Least Common Multiple:
      240 

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 = 15

Making Equivalent Fractions :

 5.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      1523
   ——————————————————  =   ————
         L.C.M             240 

   R. Mult. • R. Num.      915 • 15
   ——————————————————  =   ————————
         L.C.M               240   

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 1523 + 915 • 15     953
 ———————————————  =  ———
       240           15 

Final result :

  953            
  ——— = 63.53333 
  15