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)

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

  (2 • (10-1)) -  (4 • ((2)(-2)•(5)(-2)))

Step  2  :

Raising to a Power :

 2.1      Canceling out  2² as it appears on both sides of the fraction line

Equation at the end of step  2  :

                   1
  (2 • (10-1)) -  ——
                  25

Step  3  :

 3.1     10 = 2•5

(10)^-1 = (2•5)^(-1) = (2)^(-1) • (5)^(-1)

Equation at the end of step  3  :

                              1
  (2 • ((2)(-1)•(5)(-1))) -  ——
                             25

Step  4  :

Canceling Out :

 4.1      Canceling out  2  as it appears on both sides of the fraction line

Equation at the end of step  4  :

  1     1
  — -  ——
  5    25

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       5 

      The right denominator is :       25 

      Least Common Multiple:
      25 

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 = 5

   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.       5
   ——————————————————  =   ——
         L.C.M             25

   R. Mult. • R. Num.       1
   ——————————————————  =   ——
         L.C.M             25

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:

 5 - (1)      4
 ———————  =  ——
   25        25

Final result :

   4           
  —— = 0.16000 
  25