Solution - Adding, subtracting and finding the least common multiple

Step  1  :

            2
 Simplify   —
            3

Equation at the end of step  1  :

   5   5    1    2
  (—-(——•(3-—)))+—
   8  12    4    3

Step  2  :

            1
 Simplify   —
            4

Equation at the end of step  2  :

   5   5    1    2
  (—-(——•(3-—)))+—
   8  12    4    3

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Subtracting a fraction from a whole

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

          3     3 • 4
     3 =  —  =  —————
          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 :

 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:

 3 • 4 - (1)     11
 ———————————  =  ——
      4          4 

Equation at the end of step  3  :

   5      5   11      2
  (— -  (—— • ——)) +  —
   8     12   4       3

Step  4  :

             5
 Simplify   ——
            12

Equation at the end of step  4  :

   5      5   11      2
  (— -  (—— • ——)) +  —
   8     12   4       3

Step  5  :

            5
 Simplify   —
            8

Equation at the end of step  5  :

   5    55     2
  (— -  ——) +  —
   8    48     3

Step  6  :

Calculating the Least Common Multiple :

 6.1    Find the Least Common Multiple

      The left denominator is :       8 

      The right denominator is :       48 

      Least Common Multiple:
      48 

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 = 6

   Right_M = L.C.M / R_Deno = 1

Making Equivalent Fractions :

 6.3      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 • 6
   ——————————————————  =   —————
         L.C.M              48  

   R. Mult. • R. Num.      55
   ——————————————————  =   ——
         L.C.M             48

Adding fractions that have a common denominator :

 6.4       Adding up the two equivalent fractions

 5 • 6 - (55)     -25
 ————————————  =  ———
      48          48 

Equation at the end of step  6  :

  -25    2
  ——— +  —
  48     3

Step  7  :

Calculating the Least Common Multiple :

 7.1    Find the Least Common Multiple

      The left denominator is :       48 

      The right denominator is :       3 

      Least Common Multiple:
      48 

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 = 1

   Right_M = L.C.M / R_Deno = 16

Making Equivalent Fractions :

 7.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      -25
   ——————————————————  =   ———
         L.C.M             48 

   R. Mult. • R. Num.      2 • 16
   ——————————————————  =   ——————
         L.C.M               48  

Adding fractions that have a common denominator :

 7.4       Adding up the two equivalent fractions

 -25 + 2 • 16      7
 ————————————  =  ——
      48          48

Final result :

   7           
  —— = 0.14583 
  48