Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "4.096" was replaced by "(4096/1000)". 3 more similar replacement(s)

Step  1  :

            512
 Simplify   ———
            125

Equation at the end of step  1  :

   354       96       512
  (——— -  ({———}2) -  ———
   100      100       125

Step  2  :

            24
 Simplify   ——
            25

Equation at the end of step  2  :

   354     24        512
  (——— -  (——)2)) -  ———
   100     25        125

Step  3  :

 3.1     24 = 23•3

(24)² = (2³•3)² = 2⁶ • 3²  3.2     25 = 5² (25)² = (5²)² = 5⁴

Equation at the end of step  3  :

   354    (26•32)     512
  (——— -  ———————) -  ———
   100      54        125

Step  4  :

            177
 Simplify   ———
            50 

Equation at the end of step  4  :

   177    (26•32)     512
  (——— -  ———————) -  ———
   50       54        125

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       50 

      The right denominator is :       625 

      Least Common Multiple:
      1250 

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 = 25

   Right_M = L.C.M / R_Deno = 2

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.      177 • 25
   ——————————————————  =   ————————
         L.C.M               1250  

   R. Mult. • R. Num.      576 • 2
   ——————————————————  =   ———————
         L.C.M              1250  

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:

 177 • 25 - (576 • 2)     3273
 ————————————————————  =  ————
         1250             1250

Equation at the end of step  5  :

  3273    512
  ———— -  ———
  1250    125

Step  6  :

Calculating the Least Common Multiple :

 6.1    Find the Least Common Multiple

      The left denominator is :       1250 

      The right denominator is :       125 

      Least Common Multiple:
      1250 

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 = 10

Making Equivalent Fractions :

 6.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      3273
   ——————————————————  =   ————
         L.C.M             1250

   R. Mult. • R. Num.      512 • 10
   ——————————————————  =   ————————
         L.C.M               1250  

Adding fractions that have a common denominator :

 6.4       Adding up the two equivalent fractions

 3273 - (512 • 10)     -1847
 —————————————————  =  —————
       1250            1250 

Final result :

  -1847            
  ————— = -1.47760 
  1250