Solution - Adding, subtracting and finding the least common multiple

Step  1  :

            47
 Simplify   ——
            84

Equation at the end of step  1  :

    5    19     47
  (—— +  ——) +  ——
   14    21     84

Step  2  :

            19
 Simplify   ——
            21

Equation at the end of step  2  :

    5    19     47
  (—— +  ——) +  ——
   14    21     84

Step  3  :

             5
 Simplify   ——
            14

Equation at the end of step  3  :

    5    19     47
  (—— +  ——) +  ——
   14    21     84

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       14 

      The right denominator is :       21 

      Least Common Multiple:
      42 

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.      5 • 3
   ——————————————————  =   —————
         L.C.M              42  

   R. Mult. • R. Num.      19 • 2
   ——————————————————  =   ——————
         L.C.M               42  

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:

 5 • 3 + 19 • 2     53
 ——————————————  =  ——
       42           42

Equation at the end of step  4  :

  53    47
  —— +  ——
  42    84

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       42 

      The right denominator is :       84 

      Least Common Multiple:
      84 

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 = 2

   Right_M = L.C.M / R_Deno = 1

Making Equivalent Fractions :

 5.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      53 • 2
   ——————————————————  =   ——————
         L.C.M               84  

   R. Mult. • R. Num.      47
   ——————————————————  =   ——
         L.C.M             84

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 53 • 2 + 47     51
 ———————————  =  ——
     84          28

Final result :

  51           
  —— = 1.82143 
  28