Solution - Adding, subtracting and finding the least common multiple

Step  1  :

             7
 Simplify   ——
            36

Equation at the end of step  1  :

         1            7
  ((1 • ——) -  1) +  ——
        24           36

Step  2  :

             1
 Simplify   ——
            24

Equation at the end of step  2  :

         1            7
  ((1 • ——) -  1) +  ——
        24           36

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  24  as the denominator :

         1     1 • 24
    1 =  —  =  ——————
         1       24  

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

 3.2       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:

 1 - (24)     -23
 ————————  =  ———
    24        24 

Equation at the end of step  3  :

  -23     7
  ——— +  ——
  24     36

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       24 

      The right denominator is :       36 

      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 = 3

   Right_M = L.C.M / R_Deno = 2

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.      -23 • 3
   ——————————————————  =   ———————
         L.C.M               72   

   R. Mult. • R. Num.      7 • 2
   ——————————————————  =   —————
         L.C.M              72  

Adding fractions that have a common denominator :

 4.4       Adding up the two equivalent fractions

 -23 • 3 + 7 • 2     -55
 ———————————————  =  ———
       72            72 

Final result :

  -55            
  ——— = -0.76389 
  72