Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "264.2" was replaced by "(2642/10)". 3 more similar replacement(s)

Step  1  :

            1321
 Simplify   ————
             5  

Equation at the end of step  1  :

    5546            711     1321
  ((———— +  221) +  ———) +  ————
     10             10       5  

Step  2  :

            711
 Simplify   ———
            10 

Equation at the end of step  2  :

    5546            711     1321
  ((———— +  221) +  ———) +  ————
     10             10       5  

Step  3  :

            2773
 Simplify   ————
             5  

Equation at the end of step  3  :

    2773            711     1321
  ((———— +  221) +  ———) +  ————
     5              10       5  

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  5  as the denominator :

           221     221 • 5
    221 =  ———  =  ———————
            1         5   

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 :

 4.2       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:

 2773 + 221 • 5     3878
 ——————————————  =  ————
       5             5  

Equation at the end of step  4  :

   3878    711     1321
  (———— +  ———) +  ————
    5      10       5  

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       5 

      The right denominator is :       10 

      Least Common Multiple:
      10 

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 = 2

   Right_M = L.C.M / R_Deno = 1

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.      3878 • 2
   ——————————————————  =   ————————
         L.C.M                10   

   R. Mult. • R. Num.      711
   ——————————————————  =   ———
         L.C.M             10 

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 3878 • 2 + 711     8467
 ——————————————  =  ————
       10            10 

Equation at the end of step  5  :

  8467    1321
  ———— +  ————
   10      5  

Step  6  :

Calculating the Least Common Multiple :

 6.1    Find the Least Common Multiple

      The left denominator is :       10 

      The right denominator is :       5 

      Least Common Multiple:
      10 

Calculating Multipliers :

 6.2    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 = 2

Making Equivalent Fractions :

 6.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      8467
   ——————————————————  =   ————
         L.C.M              10 

   R. Mult. • R. Num.      1321 • 2
   ——————————————————  =   ————————
         L.C.M                10   

Adding fractions that have a common denominator :

 6.4       Adding up the two equivalent fractions

 8467 + 1321 • 2     11109
 ———————————————  =  —————
       10             10  

Final result :

  11109              
  ————— = 1110.90000 
   10