Solution - Adding, subtracting and finding the least common multiple

Step  1  :

            2
 Simplify   —
            3

Equation at the end of step  1  :

      5  4     2
  ((0-—)+—)-(0-—)
      7  9     3

Step  2  :

            4
 Simplify   —
            9

Equation at the end of step  2  :

         5     4     -2
  ((0 -  —) +  —) -  ——
         7     9     3 

Step  3  :

            5
 Simplify   —
            7

Equation at the end of step  3  :

         5     4     -2
  ((0 -  —) +  —) -  ——
         7     9     3 

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       7 

      The right denominator is :       9 

      Least Common Multiple:
      63 

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 = 9

   Right_M = L.C.M / R_Deno = 7

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.      -5 • 9
   ——————————————————  =   ——————
         L.C.M               63  

   R. Mult. • R. Num.      4 • 7
   ——————————————————  =   —————
         L.C.M              63  

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:

 -5 • 9 + 4 • 7     -17
 ——————————————  =  ———
       63           63 

Equation at the end of step  4  :

  -17    -2
  ——— -  ——
  63     3 

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       63 

      The right denominator is :       3 

      Least Common Multiple:
      63 

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 = 1

   Right_M = L.C.M / R_Deno = 21

Making Equivalent Fractions :

 5.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      -17
   ——————————————————  =   ———
         L.C.M             63 

   R. Mult. • R. Num.      -2 • 21
   ——————————————————  =   ———————
         L.C.M               63   

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 -17 - (-2 • 21)     25
 ———————————————  =  ——
       63            63

Final result :

  25           
  —— = 0.39683 
  63