Solution - Adding, subtracting and finding the least common multiple

Step  1  :

            10
 Simplify   ——
            21

Equation at the end of step  1  :

  13    10
  —— -  ——
  15    21

Step  2  :

            13
 Simplify   ——
            15

Equation at the end of step  2  :

  13    10
  —— -  ——
  15    21

Step  3  :

Calculating the Least Common Multiple :

 3.1    Find the Least Common Multiple

      The left denominator is :       15 

      The right denominator is :       21 

      Least Common Multiple:
      105 

Calculating Multipliers :

 3.2    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 = 7

   Right_M = L.C.M / R_Deno = 5

Making Equivalent Fractions :

 3.3      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.      13 • 7
   ——————————————————  =   ——————
         L.C.M              105  

   R. Mult. • R. Num.      10 • 5
   ——————————————————  =   ——————
         L.C.M              105  

Adding fractions that have a common denominator :

 3.4       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:

 13 • 7 - (10 • 5)      41
 —————————————————  =  ———
        105            105

Final result :

   41           
  ——— = 0.39048 
  105