Solution - Adding, subtracting and finding the least common multiple

Step  1  :

             8
 Simplify   ——
            21

Equation at the end of step  1  :

   3     7      8
  (— +  ——) +  ——
   8    12     21

Step  2  :

             7
 Simplify   ——
            12

Equation at the end of step  2  :

   3     7      8
  (— +  ——) +  ——
   8    12     21

Step  3  :

            3
 Simplify   —
            8

Equation at the end of step  3  :

   3     7      8
  (— +  ——) +  ——
   8    12     21

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       8 

      The right denominator is :       12 

      Least Common Multiple:
      24 

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.      3 • 3
   ——————————————————  =   —————
         L.C.M              24  

   R. Mult. • R. Num.      7 • 2
   ——————————————————  =   —————
         L.C.M              24  

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 • 3 + 7 • 2     23
 —————————————  =  ——
      24           24

Equation at the end of step  4  :

  23     8
  —— +  ——
  24    21

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       24 

      The right denominator is :       21 

      Least Common Multiple:
      168 

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 = 7

   Right_M = L.C.M / R_Deno = 8

Making Equivalent Fractions :

 5.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      23 • 7
   ——————————————————  =   ——————
         L.C.M              168  

   R. Mult. • R. Num.      8 • 8
   ——————————————————  =   —————
         L.C.M              168 

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 23 • 7 + 8 • 8     75
 ——————————————  =  ——
      168           56

Final result :

  75           
  —— = 1.33929 
  56