Solution - Adding, subtracting and finding the least common multiple

Step  1  :

            3
 Simplify   —
            4

Equation at the end of step  1  :

  71  21  21 3
  ——-(——•(——•—))
  3   4   5  4

Step  2  :

            21
 Simplify   ——
            5 

Equation at the end of step  2  :

  71     21    21   3
  —— -  (—— • (—— • —))
  3      4     5    4

Step  3  :

            21
 Simplify   ——
            4 

Equation at the end of step  3  :

  71     21   63
  —— -  (—— • ——)
  3      4    20

Step  4  :

            71
 Simplify   ——
            3 

Equation at the end of step  4  :

  71    1323
  —— -  ————
  3      80 

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       3 

      The right denominator is :       80 

      Least Common Multiple:
      240 

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 = 80

   Right_M = L.C.M / R_Deno = 3

Making Equivalent Fractions :

 5.3      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.      71 • 80
   ——————————————————  =   ———————
         L.C.M               240  

   R. Mult. • R. Num.      1323 • 3
   ——————————————————  =   ————————
         L.C.M               240   

Adding fractions that have a common denominator :

 5.4       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:

 71 • 80 - (1323 • 3)     1711
 ————————————————————  =  ————
         240              240 

Final result :

  1711           
  ———— = 7.12917 
  240