Solution - Adding, subtracting and finding the least common multiple

Step  1  :

             7
 Simplify   ——
            15

Equation at the end of step  1  :

    -5  8   4   7
  ((——+——)+——)+——
    9  19  -9  15

Step  2  :

             4
 Simplify   ——
            -9

Equation at the end of step  2  :

    -5     8      4      7
  ((—— +  ——) +  ——) +  ——
    9     19     -9     15

Step  3  :

             8
 Simplify   ——
            19

Equation at the end of step  3  :

    -5     8      4      7
  ((—— +  ——) +  ——) +  ——
    9     19     -9     15

Step  4  :

            -5
 Simplify   ——
            9 

Equation at the end of step  4  :

    -5     8      4      7
  ((—— +  ——) +  ——) +  ——
    9     19     -9     15

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       9 

      The right denominator is :       19 

      Least Common Multiple:
      171 

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 = 19

   Right_M = L.C.M / R_Deno = 9

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.      -5 • 19
   ——————————————————  =   ———————
         L.C.M               171  

   R. Mult. • R. Num.      8 • 9
   ——————————————————  =   —————
         L.C.M              171 

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:

 -5 • 19 + 8 • 9     -23
 ———————————————  =  ———
       171           171

Equation at the end of step  5  :

   -23     4      7
  (——— +  ——) +  ——
   171    -9     15

Step  6  :

Calculating the Least Common Multiple :

 6.1    Find the Least Common Multiple

      The left denominator is :       171 

      The right denominator is :       -9 

      Least Common Multiple:
      171 

Calculating Multipliers :

 6.2    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 = -19

Making Equivalent Fractions :

 6.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      -23
   ——————————————————  =   ———
         L.C.M             171

   R. Mult. • R. Num.      4 • -19
   ——————————————————  =   ———————
         L.C.M               171  

Adding fractions that have a common denominator :

 6.4       Adding up the two equivalent fractions

 -23 + 4 • -19     -11
 —————————————  =  ———
      171          19 

Equation at the end of step  6  :

  -11     7
  ——— +  ——
  19     15

Step  7  :

Calculating the Least Common Multiple :

 7.1    Find the Least Common Multiple

      The left denominator is :       19 

      The right denominator is :       15 

      Least Common Multiple:
      285 

Calculating Multipliers :

 7.2    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 = 19

Making Equivalent Fractions :

 7.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      -11 • 15
   ——————————————————  =   ————————
         L.C.M               285   

   R. Mult. • R. Num.      7 • 19
   ——————————————————  =   ——————
         L.C.M              285  

Adding fractions that have a common denominator :

 7.4       Adding up the two equivalent fractions

 -11 • 15 + 7 • 19     -32
 —————————————————  =  ———
        285            285

Final result :

  -32            
  ——— = -0.11228 
  285