Solution - Adding, subtracting and finding the least common multiple

Step  1  :

             7 
 Simplify   ———
            120

Equation at the end of step  1  :

          8     13      7 
  ((0 -  ——) +  ——) +  ———
         60     90     120

Step  2  :

            13
 Simplify   ——
            90

Equation at the end of step  2  :

          8     13      7 
  ((0 -  ——) +  ——) +  ———
         60     90     120

Step  3  :

             2
 Simplify   ——
            15

Equation at the end of step  3  :

          2     13      7 
  ((0 -  ——) +  ——) +  ———
         15     90     120

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       15 

      The right denominator is :       90 

      Least Common Multiple:
      90 

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 = 6

   Right_M = L.C.M / R_Deno = 1

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 • 6
   ——————————————————  =   ——————
         L.C.M               90  

   R. Mult. • R. Num.      13
   ——————————————————  =   ——
         L.C.M             90

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 • 6 + 13      1
 ———————————  =  ——
     90          90

Equation at the end of step  4  :

   1     7 
  —— +  ———
  90    120

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       90 

      The right denominator is :       120 

      Least Common Multiple:
      360 

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 = 4

   Right_M = L.C.M / R_Deno = 3

Making Equivalent Fractions :

 5.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.       4 
   ——————————————————  =   ———
         L.C.M             360

   R. Mult. • R. Num.      7 • 3
   ——————————————————  =   —————
         L.C.M              360 

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 4 + 7 • 3      5
 —————————  =  ——
    360        72

Final result :

   5           
  —— = 0.06944 
  72