Solution - Adding, subtracting and finding the least common multiple

Step  1  :

            4
 Simplify   —
            5

Equation at the end of step  1  :

   2       4
  —— ÷ 9 - —
  35       5

Step  2  :

             2
 Simplify   ——
            35

Equation at the end of step  2  :

   2        4
  —— ÷ 9 -  —
  35        5

Step  3  :

          2      
 Divide  ——  by  9
         35      

Equation at the end of step  3  :

   2     4
  ——— -  —
  315    5

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       315 

      The right denominator is :       5 

      Least Common Multiple:
      315 

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 = 1

   Right_M = L.C.M / R_Deno = 63

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.       2 
   ——————————————————  =   ———
         L.C.M             315

   R. Mult. • R. Num.      4 • 63
   ——————————————————  =   ——————
         L.C.M              315  

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:

 2 - (4 • 63)     -50
 ————————————  =  ———
     315          63 

Final result :

  -50            
  ——— = -0.79365 
  63