Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "8.27" was replaced by "(827/100)". 3 more similar replacement(s)

Step  1  :

            827
 Simplify   ———
            100

Equation at the end of step  1  :

   496    76     827
  (——— +  ——) +  ———
   100    10     100

Step  2  :

            38
 Simplify   ——
            5 

Equation at the end of step  2  :

   496    38     827
  (——— +  ——) +  ———
   100    5      100

Step  3  :

            124
 Simplify   ———
            25 

Equation at the end of step  3  :

   124    38     827
  (——— +  ——) +  ———
   25     5      100

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.      124
   ——————————————————  =   ———
         L.C.M             25 

   R. Mult. • R. Num.      38 • 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:

 124 + 38 • 5     314
 ————————————  =  ———
      25          25 

Equation at the end of step  4  :

  314    827
  ——— +  ———
  25     100

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       25 

      The right denominator is :       100 

      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 = 1

Making Equivalent Fractions :

 5.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      314 • 4
   ——————————————————  =   ———————
         L.C.M               100  

   R. Mult. • R. Num.      827
   ——————————————————  =   ———
         L.C.M             100

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 314 • 4 + 827     2083
 —————————————  =  ————
      100          100 

Final result :

  2083            
  ———— = 20.83000 
  100