Solution - Adding, subtracting and finding the least common multiple

Step  1  :

             1
 Simplify   ——
            10

Equation at the end of step  1  :

    1     1      1
  (—— +  ——) +  ——
   30    20     10

Step  2  :

             1
 Simplify   ——
            20

Equation at the end of step  2  :

    1     1      1
  (—— +  ——) +  ——
   30    20     10

Step  3  :

             1
 Simplify   ——
            30

Equation at the end of step  3  :

    1     1      1
  (—— +  ——) +  ——
   30    20     10

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       30 

      The right denominator is :       20 

      Least Common Multiple:
      60 

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
   ——————————————————  =   ——
         L.C.M             60

   R. Mult. • R. Num.       3
   ——————————————————  =   ——
         L.C.M             60

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 + 3      1
 —————  =  ——
  60       12

Equation at the end of step  4  :

   1     1
  —— +  ——
  12    10

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       12 

      The right denominator is :       10 

      Least Common Multiple:
      60 

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 = 6

Making Equivalent Fractions :

 5.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.       5
   ——————————————————  =   ——
         L.C.M             60

   R. Mult. • R. Num.       6
   ——————————————————  =   ——
         L.C.M             60

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 5 + 6     11
 —————  =  ——
  60       60

Final result :

  11           
  —— = 0.18333 
  60