Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "0.687" was replaced by "(687/1000)". 3 more similar replacement(s)

Step  1  :

             687
 Simplify   ————
            1000

Equation at the end of step  1  :

   429    972      687
  (——— +  ———) +  ————
   100    10      1000

Step  2  :

            486
 Simplify   ———
             5 

Equation at the end of step  2  :

   429    486      687
  (——— +  ———) +  ————
   100     5      1000

Step  3  :

            429
 Simplify   ———
            100

Equation at the end of step  3  :

   429    486      687
  (——— +  ———) +  ————
   100     5      1000

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       100 

      The right denominator is :       5 

      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 = 1

   Right_M = L.C.M / R_Deno = 20

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.      429
   ——————————————————  =   ———
         L.C.M             100

   R. Mult. • R. Num.      486 • 20
   ——————————————————  =   ————————
         L.C.M               100   

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:

 429 + 486 • 20     10149
 ——————————————  =  —————
      100            100 

Equation at the end of step  4  :

  10149     687
  ————— +  ————
   100     1000

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       100 

      The right denominator is :       1000 

      Least Common Multiple:
      1000 

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 = 10

   Right_M = L.C.M / R_Deno = 1

Making Equivalent Fractions :

 5.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      10149 • 10
   ——————————————————  =   ——————————
         L.C.M                1000   

   R. Mult. • R. Num.       687
   ——————————————————  =   ————
         L.C.M             1000

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 10149 • 10 + 687     102177
 ————————————————  =  ——————
       1000            1000 

Final result :

  102177             
  —————— = 102.17700 
   1000