Solution - Adding, subtracting and finding the least common multiple

Step  1  :

            31
 Simplify   ——
            2 

Equation at the end of step  1  :

        47    31      31
  (6 • (—— -  ——)) +  ——
        8     2       2 

Step  2  :

            31
 Simplify   ——
            2 

Equation at the end of step  2  :

        47    31      31
  (6 • (—— -  ——)) +  ——
        8     2       2 

Step  3  :

            47
 Simplify   ——
            8 

Equation at the end of step  3  :

        47    31      31
  (6 • (—— -  ——)) +  ——
        8     2       2 

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       8 

      The right denominator is :       2 

      Least Common Multiple:
      8 

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 = 1

   Right_M = L.C.M / R_Deno = 4

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.      47
   ——————————————————  =   ——
         L.C.M             8 

   R. Mult. • R. Num.      31 • 4
   ——————————————————  =   ——————
         L.C.M               8   

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:

 47 - (31 • 4)     -77
 —————————————  =  ———
       8            8 

Equation at the end of step  4  :

       -77     31
  (6 • ———) +  ——
        8      2 

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       4 

      The right denominator is :       2 

      Least Common Multiple:
      4 

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 = 1

   Right_M = L.C.M / R_Deno = 2

Making Equivalent Fractions :

 5.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      -231
   ——————————————————  =   ————
         L.C.M              4  

   R. Mult. • R. Num.      31 • 2
   ——————————————————  =   ——————
         L.C.M               4   

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 -231 + 31 • 2     -169
 —————————————  =  ————
       4            4  

Final result :

  -169             
  ———— = -42.25000 
   4