Solution - Adding, subtracting and finding the least common multiple

Step  1  :

            61
 Simplify   ——
            4 

Equation at the end of step  1  :

   51    75     61
  (—— +  ——) +  ——
   3     6      4 

Step  2  :

            25
 Simplify   ——
            2 

Equation at the end of step  2  :

   51    25     61
  (—— +  ——) +  ——
   3     2      4 

Step  3  :

            17
 Simplify   ——
            1 

Equation at the end of step  3  :

         25     61
  (17 +  ——) +  ——
         2      4 

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Adding a fraction to a whole

Rewrite the whole as a fraction using  2  as the denominator :

           17     17 • 2
     17 =  ——  =  ——————
           1        2   

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 :

 4.2       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 • 2 + 25     59
 ———————————  =  ——
      2          2 

Equation at the end of step  4  :

  59    61
  —— +  ——
  2     4 

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       2 

      The right denominator is :       4 

      Least Common Multiple:
      4 

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 = 1

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.      59 • 2
   ——————————————————  =   ——————
         L.C.M               4   

   R. Mult. • R. Num.      61
   ——————————————————  =   ——
         L.C.M             4 

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 59 • 2 + 61     179
 ———————————  =  ———
      4           4 

Final result :

  179            
  ——— = 44.75000 
   4