Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-3" was replaced by "^(-3)".

(2): "0.00065" was replaced by "(00065/100000)". 2 more similar replacement(s)

Step  1  :

              13 
 Simplify   —————
            20000

Equation at the end of step  1  :

   28                13 
  (—— • (10-3)) -  —————
   10              20000

Step  2  :

 2.1     10 = 2•5

(10)^-3 = (2•5)^(-3) = (2)^(-3) • (5)^(-3)

Equation at the end of step  2  :

   28                           13 
  (—— • ((2)(-3)•(5)(-3))) -  —————
   10                         20000

Step  3  :

            14
 Simplify   ——
            5 

Equation at the end of step  3  :

   14                           13 
  (—— • ((2)(-3)•(5)(-3))) -  —————
   5                          20000

Step  4  :

Multiplying exponents :

 4.1    5¹  multiplied by  5³   = 5^{(1 + 3)} = 5⁴

Dividing exponents :

 4.2    2¹   divided by   2³   = 2^{(1 - 3)} = 2^(-2) = ¹/_2²

Equation at the end of step  4  :

    7       13 
  ———— -  —————
  2500    20000

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       2500 

      The right denominator is :       20000 

      Least Common Multiple:
      20000 

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 = 8

   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.      7 • 8
   ——————————————————  =   —————
         L.C.M             20000

   R. Mult. • R. Num.        13 
   ——————————————————  =   —————
         L.C.M             20000

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:

 7 • 8 - (13)       43 
 ————————————  =  —————
    20000         20000

Final result :

    43            
  ————— = 0.00215 
  20000