Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "2.6" was replaced by "(26/10)". 2 more similar replacement(s)

Step  1  :

            13
 Simplify   ——
            5 

Equation at the end of step  1  :

   405          13
  (——— +  2) +  ——
   10           5 

Step  2  :

            81
 Simplify   ——
            2 

Equation at the end of step  2  :

   81          13
  (—— +  2) +  ——
   2           5 

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  2  as the denominator :

         2     2 • 2
    2 =  —  =  —————
         1       2  

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

 3.2       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:

 81 + 2 • 2     85
 ——————————  =  ——
     2          2 

Equation at the end of step  3  :

  85    13
  —— +  ——
  2     5 

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       2 

      The right denominator is :       5 

      Least Common Multiple:
      10 

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 = 5

   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.      85 • 5
   ——————————————————  =   ——————
         L.C.M               10  

   R. Mult. • R. Num.      13 • 2
   ——————————————————  =   ——————
         L.C.M               10  

Adding fractions that have a common denominator :

 4.4       Adding up the two equivalent fractions

 85 • 5 + 13 • 2     451
 ———————————————  =  ———
       10            10 

Final result :

  451            
  ——— = 45.10000 
  10