Solution - Adding, subtracting and finding the least common multiple

Step  1  :

             1
 Simplify   ——
            52

Equation at the end of step  1  :

    1    1      1
  (—— +  —) -  ——
   13    4     52

Step  2  :

            1
 Simplify   —
            4

Equation at the end of step  2  :

    1    1      1
  (—— +  —) -  ——
   13    4     52

Step  3  :

             1
 Simplify   ——
            13

Equation at the end of step  3  :

    1    1      1
  (—— +  —) -  ——
   13    4     52

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       13 

      The right denominator is :       4 

      Least Common Multiple:
      52 

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 = 4

   Right_M = L.C.M / R_Deno = 13

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.       4
   ——————————————————  =   ——
         L.C.M             52

   R. Mult. • R. Num.      13
   ——————————————————  =   ——
         L.C.M             52

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:

 4 + 13     17
 ——————  =  ——
   52       52

Equation at the end of step  4  :

  17     1
  —— -  ——
  52    52

Step  5  :

Adding fractions which have a common denominator :

 5.1       Adding fractions which 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 - (1)      4
 ————————  =  ——
    52        13

Final result :

   4           
  —— = 0.30769 
  13