Solution - Adding, subtracting and finding the least common multiple

Step  1  :

             5
 Simplify   ——
            24

Equation at the end of step  1  :

  3     1          5
  — -  (— • (0 -  ——))
  4     3         24

Step  2  :

            1
 Simplify   —
            3

Equation at the end of step  2  :

  3     1   -5
  — -  (— • ——)
  4     3   24

Step  3  :

            3
 Simplify   —
            4

Equation at the end of step  3  :

  3    -5
  — -  ——
  4    72

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       4 

      The right denominator is :       72 

      Least Common Multiple:
      72 

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 = 18

   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.      3 • 18
   ——————————————————  =   ——————
         L.C.M               72  

   R. Mult. • R. Num.      -5
   ——————————————————  =   ——
         L.C.M             72

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:

 3 • 18 - (-5)     59
 —————————————  =  ——
      72           72

Final result :

  59           
  —— = 0.81944 
  72