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): "5.5" was replaced by "(55/10)". 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  :

   24          55
  (——•(10-1))-(——•((2)(-2)•(5)(-2)))
   10          10

Step  2  :

            11
 Simplify   ——
            2 

Equation at the end of step  2  :

   24               11
  (—— • (10-1)) -  (—— • ((2)(-2)•(5)(-2)))
   10               2 

Step  3  :

Raising to a Power :

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

Equation at the end of step  3  :

   24               11
  (—— • (10-1)) -  ———
   10              200

Step  4  :

 4.1     10 = 2•5

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

Equation at the end of step  4  :

   24                          11
  (—— • ((2)(-1)•(5)(-1))) -  ———
   10                         200

Step  5  :

            12
 Simplify   ——
            5 

Equation at the end of step  5  :

   12                          11
  (—— • ((2)(-1)•(5)(-1))) -  ———
   5                          200

Step  6  :

Multiplying exponents :

 6.1    5¹  multiplied by  5¹   = 5^{(1 + 1)} = 5²

Dividing exponents :

 6.2    2²   divided by   2¹   = 2^{(2 - 1)} = 2¹ = 2

Equation at the end of step  6  :

   6     11
  —— -  ———
  25    200

Step  7  :

Calculating the Least Common Multiple :

 7.1    Find the Least Common Multiple

      The left denominator is :       25 

      The right denominator is :       200 

      Least Common Multiple:
      200 

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 = 8

   Right_M = L.C.M / R_Deno = 1

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.      6 • 8
   ——————————————————  =   —————
         L.C.M              200 

   R. Mult. • R. Num.       11
   ——————————————————  =   ———
         L.C.M             200

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:

 6 • 8 - (11)      37
 ————————————  =  ———
     200          200

Final result :

   37           
  ——— = 0.18500 
  200