Solution - Adding, subtracting and finding the least common multiple

Step  1  :

             5
 Simplify   ——
            14

Equation at the end of step  1  :

    9    4      5
  (—— -  —) -  ——
   35    7     14

Step  2  :

            4
 Simplify   —
            7

Equation at the end of step  2  :

    9    4      5
  (—— -  —) -  ——
   35    7     14

Step  3  :

             9
 Simplify   ——
            35

Equation at the end of step  3  :

    9    4      5
  (—— -  —) -  ——
   35    7     14

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       35 

      The right denominator is :       7 

      Least Common Multiple:
      35 

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 = 5

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.       9
   ——————————————————  =   ——
         L.C.M             35

   R. Mult. • R. Num.      4 • 5
   ——————————————————  =   —————
         L.C.M              35  

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:

 9 - (4 • 5)     -11
 ———————————  =  ———
     35          35 

Equation at the end of step  4  :

  -11     5
  ——— -  ——
  35     14

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       35 

      The right denominator is :       14 

      Least Common Multiple:
      70 

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 = 2

   Right_M = L.C.M / R_Deno = 5

Making Equivalent Fractions :

 5.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      -11 • 2
   ——————————————————  =   ———————
         L.C.M               70   

   R. Mult. • R. Num.      5 • 5
   ——————————————————  =   —————
         L.C.M              70  

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 -11 • 2 - (5 • 5)     -47
 —————————————————  =  ———
        70             70 

Final result :

  -47            
  ——— = -0.67143 
  70