Solution - Adding, subtracting and finding the least common multiple

Step  1  :

            5
 Simplify   —
            6

Equation at the end of step  1  :

           5            5
  ((17 -  ——) -  14) -  —
          12            6

Step  2  :

             5
 Simplify   ——
            12

Equation at the end of step  2  :

           5            5
  ((17 -  ——) -  14) -  —
          12            6

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  12  as the denominator :

           17     17 • 12
     17 =  ——  =  ———————
           1        12   

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:

 17 • 12 - (5)     199
 —————————————  =  ———
      12           12 

Equation at the end of step  3  :

   199           5
  (——— -  14) -  —
   12            6

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  12  as the denominator :

          14     14 • 12
    14 =  ——  =  ———————
          1        12   

Adding fractions that have a common denominator :

 4.2       Adding up the two equivalent fractions

 199 - (14 • 12)     31
 ———————————————  =  ——
       12            12

Equation at the end of step  4  :

  31    5
  —— -  —
  12    6

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       12 

      The right denominator is :       6 

      Least Common Multiple:
      12 

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.      31
   ——————————————————  =   ——
         L.C.M             12

   R. Mult. • R. Num.      5 • 2
   ——————————————————  =   —————
         L.C.M              12  

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 31 - (5 • 2)     7
 ————————————  =  —
      12          4

Final result :

  7           
  — = 1.75000 
  4