Solution - Adding, subtracting and finding the least common multiple

Step  1  :

            3
 Simplify   —
            7

Equation at the end of step  1  :

   1       3
  —— ÷ 7 - —
  22       7

Step  2  :

             1
 Simplify   ——
            22

Equation at the end of step  2  :

   1        3
  —— ÷ 7 -  —
  22        7

Step  3  :

          1      
 Divide  ——  by  7
         22      

Equation at the end of step  3  :

   1     3
  ——— -  —
  154    7

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       154 

      The right denominator is :       7 

      Least Common Multiple:
      154 

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 = 22

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.       1 
   ——————————————————  =   ———
         L.C.M             154

   R. Mult. • R. Num.      3 • 22
   ——————————————————  =   ——————
         L.C.M              154  

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:

 1 - (3 • 22)     -65
 ————————————  =  ———
     154          154

Final result :

  -65            
  ——— = -0.42208 
  154