Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "4.5" was replaced by "(45/10)". 4 more similar replacement(s)

Step  1  :

            9
 Simplify   —
            2

Equation at the end of step  1  :

    411 155   89  9
  ((———+———)+———)+—
    100 10   100  2

Step  2  :

             89
 Simplify   ———
            100

Equation at the end of step  2  :

    411    155      89     9
  ((——— +  ———) +  ———) +  —
    100    10      100     2

Step  3  :

            31
 Simplify   ——
            2 

Equation at the end of step  3  :

    411    31      89     9
  ((——— +  ——) +  ———) +  —
    100    2      100     2

Step  4  :

            411
 Simplify   ———
            100

Equation at the end of step  4  :

    411    31      89     9
  ((——— +  ——) +  ———) +  —
    100    2      100     2

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       100 

      The right denominator is :       2 

      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 = 1

   Right_M = L.C.M / R_Deno = 50

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.      411
   ——————————————————  =   ———
         L.C.M             100

   R. Mult. • R. Num.      31 • 50
   ——————————————————  =   ———————
         L.C.M               100  

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:

 411 + 31 • 50     1961
 —————————————  =  ————
      100          100 

Equation at the end of step  5  :

   1961     89     9
  (———— +  ———) +  —
   100     100     2

Step  6  :

Adding fractions which have a common denominator :

 6.1       Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

 1961 + 89     41
 —————————  =  ——
    100        2 

Equation at the end of step  6  :

  41    9
  —— +  —
  2     2

Step  7  :

Adding fractions which have a common denominator :

 7.1       Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

 41 + 9     25
 ——————  =  ——
   2        1 

Final result :

  25