Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "1.65" was replaced by "(165/100)". 3 more similar replacement(s)

Step  1  :

            33
 Simplify   ——
            20

Equation at the end of step  1  :

   108     4     33
  (——— +  ——) +  ——
   100    10     20

Step  2  :

            2
 Simplify   —
            5

Equation at the end of step  2  :

   108    2     33
  (——— +  —) +  ——
   100    5     20

Step  3  :

            27
 Simplify   ——
            25

Equation at the end of step  3  :

   27    2     33
  (—— +  —) +  ——
   25    5     20

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       25 

      The right denominator is :       5 

      Least Common Multiple:
      25 

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 = 1

   Right_M = L.C.M / R_Deno = 5

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.      27
   ——————————————————  =   ——
         L.C.M             25

   R. Mult. • R. Num.      2 • 5
   ——————————————————  =   —————
         L.C.M              25  

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:

 27 + 2 • 5     37
 ——————————  =  ——
     25         25

Equation at the end of step  4  :

  37    33
  —— +  ——
  25    20

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       25 

      The right denominator is :       20 

      Least Common Multiple:
      100 

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 = 4

   Right_M = L.C.M / R_Deno = 5

Making Equivalent Fractions :

 5.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      37 • 4
   ——————————————————  =   ——————
         L.C.M              100  

   R. Mult. • R. Num.      33 • 5
   ——————————————————  =   ——————
         L.C.M              100  

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 37 • 4 + 33 • 5     313
 ———————————————  =  ———
       100           100

Final result :

  313           
  ——— = 3.13000 
  100