Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "6.89" was replaced by "(689/100)". 2 more similar replacement(s)

Step  1  :

            689
 Simplify   ———
            100

Equation at the end of step  1  :

   172          689
  (——— +  7) +  ———
   10           100

Step  2  :

            86
 Simplify   ——
            5 

Equation at the end of step  2  :

   86          689
  (—— +  7) +  ———
   5           100

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Adding a whole to a fraction

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

         7     7 • 5
    7 =  —  =  —————
         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 :

 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:

 86 + 7 • 5     121
 ——————————  =  ———
     5           5 

Equation at the end of step  3  :

  121    689
  ——— +  ———
   5     100

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       5 

      The right denominator is :       100 

      Least Common Multiple:
      100 

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 = 20

   Right_M = L.C.M / R_Deno = 1

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.      121 • 20
   ——————————————————  =   ————————
         L.C.M               100   

   R. Mult. • R. Num.      689
   ——————————————————  =   ———
         L.C.M             100

Adding fractions that have a common denominator :

 4.4       Adding up the two equivalent fractions

 121 • 20 + 689     3109
 ——————————————  =  ————
      100           100 

Final result :

  3109            
  ———— = 31.09000 
  100