Solution - Adding, subtracting and finding the least common multiple

Step  1  :

            367
 Simplify   ———
             5 

Equation at the end of step  1  :

  422       367
  ——— ÷ 7 - ——— ÷ 9
   3         5 

Step  2  :

         367      
 Divide  ———  by  9
          5       

Equation at the end of step  2  :

  422       367
  ——— ÷ 7 - ———
   3        45 

Step  3  :

            422
 Simplify   ———
             3 

Equation at the end of step  3  :

  422        367
  ——— ÷ 7 -  ———
   3         45 

Step  4  :

         422      
 Divide  ———  by  7
          3       

Equation at the end of step  4  :

  422    367
  ——— -  ———
  21     45 

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       21 

      The right denominator is :       45 

      Least Common Multiple:
      315 

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 = 15

   Right_M = L.C.M / R_Deno = 7

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.      422 • 15
   ——————————————————  =   ————————
         L.C.M               315   

   R. Mult. • R. Num.      367 • 7
   ——————————————————  =   ———————
         L.C.M               315  

Adding fractions that have a common denominator :

 5.4       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:

 422 • 15 - (367 • 7)     3761
 ————————————————————  =  ————
         315              315 

Final result :

  3761            
  ———— = 11.93968 
  315