Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "4.94" was replaced by "(494/100)". 4 more similar replacement(s)

Step  1  :

            247
 Simplify   ———
            50 

Equation at the end of step  1  :

     6  45  29  247
  ((——+———)+——)+———
    10 100  10  50 

Step  2  :

            29
 Simplify   ——
            10

Equation at the end of step  2  :

     6     45     29     247
  ((—— +  ———) +  ——) +  ———
    10    100     10     50 

Step  3  :

             9
 Simplify   ——
            20

Equation at the end of step  3  :

     6     9     29     247
  ((—— +  ——) +  ——) +  ———
    10    20     10     50 

Step  4  :

            3
 Simplify   —
            5

Equation at the end of step  4  :

    3     9     29     247
  ((— +  ——) +  ——) +  ———
    5    20     10     50 

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       5 

      The right denominator is :       20 

      Least Common Multiple:
      20 

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

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.      3 • 4
   ——————————————————  =   —————
         L.C.M              20  

   R. Mult. • R. Num.       9
   ——————————————————  =   ——
         L.C.M             20

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:

 3 • 4 + 9     21
 —————————  =  ——
    20         20

Equation at the end of step  5  :

   21    29     247
  (—— +  ——) +  ———
   20    10     50 

Step  6  :

Calculating the Least Common Multiple :

 6.1    Find the Least Common Multiple

      The left denominator is :       20 

      The right denominator is :       10 

      Least Common Multiple:
      20 

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.      21
   ——————————————————  =   ——
         L.C.M             20

   R. Mult. • R. Num.      29 • 2
   ——————————————————  =   ——————
         L.C.M               20  

Adding fractions that have a common denominator :

 6.4       Adding up the two equivalent fractions

 21 + 29 • 2     79
 ———————————  =  ——
     20          20

Equation at the end of step  6  :

  79    247
  —— +  ———
  20    50 

Step  7  :

Calculating the Least Common Multiple :

 7.1    Find the Least Common Multiple

      The left denominator is :       20 

      The right denominator is :       50 

      Least Common Multiple:
      100 

Calculating Multipliers :

 7.2    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 :

 7.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      79 • 5
   ——————————————————  =   ——————
         L.C.M              100  

   R. Mult. • R. Num.      247 • 2
   ——————————————————  =   ———————
         L.C.M               100  

Adding fractions that have a common denominator :

 7.4       Adding up the two equivalent fractions

 79 • 5 + 247 • 2     889
 ————————————————  =  ———
       100            100

Final result :

  889           
  ——— = 8.89000 
  100