Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "6.79" was replaced by "(679/100)". 3 more similar replacement(s)

Step  1  :

            679
 Simplify   ———
            100

Equation at the end of step  1  :

    5746           432     679
  ((———— +  31) +  ———) +  ———
    100            10      100

Step  2  :

            216
 Simplify   ———
             5 

Equation at the end of step  2  :

    5746           216     679
  ((———— +  31) +  ———) +  ———
    100             5      100

Step  3  :

            2873
 Simplify   ————
             50 

Equation at the end of step  3  :

    2873           216     679
  ((———— +  31) +  ———) +  ———
     50             5      100

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  50  as the denominator :

          31     31 • 50
    31 =  ——  =  ———————
          1        50   

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:

 2873 + 31 • 50     4423
 ——————————————  =  ————
       50            50 

Equation at the end of step  4  :

   4423    216     679
  (———— +  ———) +  ———
    50      5      100

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       50 

      The right denominator is :       5 

      Least Common Multiple:
      50 

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 = 10

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.      4423
   ——————————————————  =   ————
         L.C.M              50 

   R. Mult. • R. Num.      216 • 10
   ——————————————————  =   ————————
         L.C.M                50   

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 4423 + 216 • 10     6583
 ———————————————  =  ————
       50             50 

Equation at the end of step  5  :

  6583    679
  ———— +  ———
   50     100

Step  6  :

Calculating the Least Common Multiple :

 6.1    Find the Least Common Multiple

      The left denominator is :       50 

      The right denominator is :       100 

      Least Common Multiple:
      100 

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 = 2

   Right_M = L.C.M / R_Deno = 1

Making Equivalent Fractions :

 6.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      6583 • 2
   ——————————————————  =   ————————
         L.C.M               100   

   R. Mult. • R. Num.      679
   ——————————————————  =   ———
         L.C.M             100

Adding fractions that have a common denominator :

 6.4       Adding up the two equivalent fractions

 6583 • 2 + 679     2769
 ——————————————  =  ————
      100            20 

Final result :

  2769             
  ———— = 138.45000 
   20