Solution - Adding, subtracting and finding the least common multiple

Step  1  :

             5
 Simplify   ——
            16

Equation at the end of step  1  :

           5            5
  ((14 -  ——) -  3) -  ——
          32           16

Step  2  :

             5
 Simplify   ——
            32

Equation at the end of step  2  :

           5            5
  ((14 -  ——) -  3) -  ——
          32           16

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  32  as the denominator :

           14     14 • 32
     14 =  ——  =  ———————
           1        32   

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

 3.2       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:

 14 • 32 - (5)     443
 —————————————  =  ———
      32           32 

Equation at the end of step  3  :

   443           5
  (——— -  3) -  ——
   32           16

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  32  as the denominator :

         3     3 • 32
    3 =  —  =  ——————
         1       32  

Adding fractions that have a common denominator :

 4.2       Adding up the two equivalent fractions

 443 - (3 • 32)     347
 ——————————————  =  ———
       32           32 

Equation at the end of step  4  :

  347     5
  ——— -  ——
  32     16

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       32 

      The right denominator is :       16 

      Least Common Multiple:
      32 

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 = 2

Making Equivalent Fractions :

 5.3      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.      347
   ——————————————————  =   ———
         L.C.M             32 

   R. Mult. • R. Num.      5 • 2
   ——————————————————  =   —————
         L.C.M              32  

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 347 - (5 • 2)     337
 —————————————  =  ———
      32           32 

Final result :

  337            
  ——— = 10.53125 
  32