Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "0.005" was replaced by "(005/1000)". 3 more similar replacement(s)

Step  1  :

             1 
 Simplify   ———
            200

Equation at the end of step  1  :

    31    115       1 
  ((—— -  ———)2) ÷ ———
    10    100      200

Step  2  :

            23
 Simplify   ——
            20

Equation at the end of step  2  :

    31    23       1 
  ((—— -  ——)2) ÷ ———
    10    20      200

Step  3  :

            31
 Simplify   ——
            10

Equation at the end of step  3  :

  31   23       1 
  —— - ——)2) ÷ ———
  10   20      200

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       10 

      The right denominator is :       20 

      Least Common Multiple:
      20 

Calculating Multipliers :

 4.2    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 = 1

Making Equivalent Fractions :

 4.3      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.      31 • 2
   ——————————————————  =   ——————
         L.C.M               20  

   R. Mult. • R. Num.      23
   ——————————————————  =   ——
         L.C.M             20

Adding fractions that have a common denominator :

 4.4       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:

 31 • 2 - (23)     39
 —————————————  =  ——
      20           20

Equation at the end of step  4  :

  39       1 
 (——)2) ÷ ———
  20      200

Step  5  :

 5.1     39 = 3•13

(39)² = (3•13)² = 3² • 13²  5.2     20 = 2²•5 (20)² = (2²•5)² = 2⁴ • 5²

Equation at the end of step  5  :

  (32•132)    1 
  ———————— ÷ ———
  (24•52)    200

Step  6  :

         (32•132)       1 
 Divide  ————————  by  ———
         (24•52)       200

 6.1    Dividing fractions

To divide fractions, write the divison as multiplication by the reciprocal of the divisor :

(32•132)      1        (32•132)     200
————————  ÷  ———   =   ————————  •  ———
(24•52)      200       (24•52)       1 

Dividing exponents :

 6.2    2³   divided by   2⁴   = 2^{(3 - 4)} = 2^(-1) = ¹/_2¹ = ¹/₂

Canceling Out :

 6.3      Canceling out  5² as it appears on both sides of the fraction line

Final result :

  1521             
  ———— = 760.50000 
   2