Solution - Adding, subtracting and finding the least common multiple

Step  1  :

            13
 Simplify   ——
            16

Equation at the end of step  1  :

   3 13
  ——+—— ÷ 29 ÷ 15 ÷ 11 ÷ 3
  16 16

Step  2  :

         13      
 Divide  ——  by  29
         16      

Equation at the end of step  2  :

   3     13
  —— +  ——— ÷ 15 ÷ 11 ÷ 3
  16    464

Step  3  :

          13      
 Divide  ———  by  15
         464      

Equation at the end of step  3  :

   3     13 
  —— +  ———— ÷ 11 ÷ 3
  16    6960

Step  4  :

          13       
 Divide  ————  by  11
         6960      

Equation at the end of step  4  :

   3      13 
  —— +  ————— ÷ 3
  16    76560

Step  5  :

           13       
 Divide  —————  by  3
         76560      

Equation at the end of step  5  :

   3      13  
  —— +  ——————
  16    229680

Step  6  :

             3
 Simplify   ——
            16

Equation at the end of step  6  :

   3      13  
  —— +  ——————
  16    229680

Step  7  :

Calculating the Least Common Multiple :

 7.1    Find the Least Common Multiple

      The left denominator is :       16 

      The right denominator is :       229680 

      Least Common Multiple:
      229680 

Calculating Multipliers :

 7.2    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 = 14355

   Right_M = L.C.M / R_Deno = 1

Making Equivalent Fractions :

 7.3      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.      3 • 14355
   ——————————————————  =   —————————
         L.C.M              229680  

   R. Mult. • R. Num.        13  
   ——————————————————  =   ——————
         L.C.M             229680

Adding fractions that have a common denominator :

 7.4       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:

 3 • 14355 + 13      21539
 ——————————————  =  ——————
     229680         114840

Final result :

   21539           
  —————— = 0.18756 
  114840