Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-2" was replaced by "^(-2)".

(2): "4.5" was replaced by "(45/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

  1034     45
  ———— -  (—— • ((2)(-2)•(5)(-2)))
  1000     10

Step  2  :

            9
 Simplify   —
            2

Equation at the end of step  2  :

  1034     9
  ———— -  (— • ((2)(-2)•(5)(-2)))
  1000     2

Step  3  :

Multiplying exponents :

 3.1    2¹  multiplied by  2²   = 2^{(1 + 2)} = 2³

Equation at the end of step  3  :

  1034     9 
  ———— -  ———
  1000    200

Step  4  :

            517
 Simplify   ———
            500

Equation at the end of step  4  :

  517     9 
  ——— -  ———
  500    200

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       500 

      The right denominator is :       200 

      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 = 2

   Right_M = L.C.M / R_Deno = 5

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.      517 • 2
   ——————————————————  =   ———————
         L.C.M              1000  

   R. Mult. • R. Num.      9 • 5
   ——————————————————  =   —————
         L.C.M             1000 

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:

 517 • 2 - (9 • 5)      989
 —————————————————  =  ————
       1000            1000

Final result :

   989           
  ———— = 0.98900 
  1000