Solution - Adding, subtracting and finding the least common multiple

Step  1  :

            1
 Simplify   —
            4

Equation at the end of step  1  :

      1     1      1
  ((2-—)+(3-—))+(4-—)
      2     3      4

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  4  as the denominator :

          4     4 • 4
     4 =  —  =  —————
          1       4  

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 :

 2.2       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:

 4 • 4 - (1)     15
 ———————————  =  ——
      4          4 

Equation at the end of step  2  :

      1     1   15
  ((2-—)+(3-—))+——
      2     3   4 

Step  3  :

            1
 Simplify   —
            3

Equation at the end of step  3  :

         1           1      15
  ((2 -  —) +  (3 -  —)) +  ——
         2           3      4 

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  3  as the denominator :

          3     3 • 3
     3 =  —  =  —————
          1       3  

Adding fractions that have a common denominator :

 4.2       Adding up the two equivalent fractions

 3 • 3 - (1)     8
 ———————————  =  —
      3          3

Equation at the end of step  4  :

         1     8     15
  ((2 -  —) +  —) +  ——
         2     3     4 

Step  5  :

            1
 Simplify   —
            2

Equation at the end of step  5  :

         1     8     15
  ((2 -  —) +  —) +  ——
         2     3     4 

Step  6  :

Rewriting the whole as an Equivalent Fraction :

 6.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  2  as the denominator :

          2     2 • 2
     2 =  —  =  —————
          1       2  

Adding fractions that have a common denominator :

 6.2       Adding up the two equivalent fractions

 2 • 2 - (1)     3
 ———————————  =  —
      2          2

Equation at the end of step  6  :

   3    8     15
  (— +  —) +  ——
   2    3     4 

Step  7  :

Calculating the Least Common Multiple :

 7.1    Find the Least Common Multiple

      The left denominator is :       2 

      The right denominator is :       3 

      Least Common Multiple:
      6 

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 = 3

   Right_M = L.C.M / R_Deno = 2

Making Equivalent Fractions :

 7.3      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 • 3
   ——————————————————  =   —————
         L.C.M               6  

   R. Mult. • R. Num.      8 • 2
   ——————————————————  =   —————
         L.C.M               6  

Adding fractions that have a common denominator :

 7.4       Adding up the two equivalent fractions

 3 • 3 + 8 • 2     25
 —————————————  =  ——
       6           6 

Equation at the end of step  7  :

  25    15
  —— +  ——
  6     4 

Step  8  :

Calculating the Least Common Multiple :

 8.1    Find the Least Common Multiple

      The left denominator is :       6 

      The right denominator is :       4 

      Least Common Multiple:
      12 

Calculating Multipliers :

 8.2    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 = 3

Making Equivalent Fractions :

 8.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      25 • 2
   ——————————————————  =   ——————
         L.C.M               12  

   R. Mult. • R. Num.      15 • 3
   ——————————————————  =   ——————
         L.C.M               12  

Adding fractions that have a common denominator :

 8.4       Adding up the two equivalent fractions

 25 • 2 + 15 • 3     95
 ———————————————  =  ——
       12            12

Final result :

  95           
  —— = 7.91667 
  12