Solution - Adding, subtracting and finding the least common multiple

Step  1  :

             9
 Simplify   ——
            10

Equation at the end of step  1  :

    2     5      9
  (—— +  ——) +  ——
   27    18     10

Step  2  :

             5
 Simplify   ——
            18

Equation at the end of step  2  :

    2     5      9
  (—— +  ——) +  ——
   27    18     10

Step  3  :

             2
 Simplify   ——
            27

Equation at the end of step  3  :

    2     5      9
  (—— +  ——) +  ——
   27    18     10

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       27 

      The right denominator is :       18 

      Least Common Multiple:
      54 

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 = 2

   Right_M = L.C.M / R_Deno = 3

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.      2 • 2
   ——————————————————  =   —————
         L.C.M              54  

   R. Mult. • R. Num.      5 • 3
   ——————————————————  =   —————
         L.C.M              54  

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:

 2 • 2 + 5 • 3     19
 —————————————  =  ——
      54           54

Equation at the end of step  4  :

  19     9
  —— +  ——
  54    10

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       54 

      The right denominator is :       10 

      Least Common Multiple:
      270 

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 = 5

   Right_M = L.C.M / R_Deno = 27

Making Equivalent Fractions :

 5.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      19 • 5
   ——————————————————  =   ——————
         L.C.M              270  

   R. Mult. • R. Num.      9 • 27
   ——————————————————  =   ——————
         L.C.M              270  

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 19 • 5 + 9 • 27     169
 ———————————————  =  ———
       270           135

Final result :

  169           
  ——— = 1.25185 
  135