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)". 1 more similar replacement(s)

(2): "2.5" was replaced by "(25/10)". 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  :

   35          25
  (——•(10-3))-(——•((2)(-2)•(5)(-2)))
   10          10

Step  2  :

            5
 Simplify   —
            2

Equation at the end of step  2  :

   35               5
  (—— • (10-3)) -  (— • ((2)(-2)•(5)(-2)))
   10               2

Step  3  :

Multiplying exponents :

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

Raising to a Power :

 3.2    5¹   divided by   5²   = 5^{(1 - 2)} = 5^(-1) = ¹/_5¹ = ¹/₅

Equation at the end of step  3  :

   35               1
  (—— • (10-3)) -  ——
   10              40

Step  4  :

 4.1     10 = 2•5

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

Equation at the end of step  4  :

   35                          1
  (—— • ((2)(-3)•(5)(-3))) -  ——
   10                         40

Step  5  :

            7
 Simplify   —
            2

Equation at the end of step  5  :

   7                          1
  (— • ((2)(-3)•(5)(-3))) -  ——
   2                         40

Step  6  :

Multiplying exponents :

 6.1    2¹  multiplied by  2³   = 2^{(1 + 3)} = 2⁴

Equation at the end of step  6  :

    7      1
  ———— -  ——
  2000    40

Step  7  :

Calculating the Least Common Multiple :

 7.1    Find the Least Common Multiple

      The left denominator is :       2000 

      The right denominator is :       40 

      Least Common Multiple:
      2000 

Calculating Multipliers :

 7.2    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 = 50

Making Equivalent Fractions :

 7.3      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 
   ——————————————————  =   ————
         L.C.M             2000

   R. Mult. • R. Num.       50 
   ——————————————————  =   ————
         L.C.M             2000

Adding fractions that have a common denominator :

 7.4       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 - (50)      -43
 ————————  =  ————
   2000       2000

Final result :

   -43            
  ———— = -0.02150 
  2000