Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "25.1" was replaced by "(251/10)". 2 more similar replacement(s)

Step  1  :

            251
 Simplify   ———
            10 

Equation at the end of step  1  :

   201     251
  {———}2 + ———) + 3
   10      10 

Step  2  :

            201
 Simplify   ———
            10 

Equation at the end of step  2  :

    201       251     
  ((———)2) +  ———) +  3
    10        10      

Step  3  :

 3.1     201 = 3•67

(201)² = (3•67)² = 3² • 67²  3.2     10 = 2•5 (10)² = (2•5)² = 2² • 5²

Equation at the end of step  3  :

   (32•672)    251     
  (———————— +  ———) +  3
   (22•52)     10      

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       100 

      The right denominator is :       10 

      Least Common Multiple:
      100 

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 = 1

   Right_M = L.C.M / R_Deno = 10

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.      (32•672)
   ——————————————————  =   ————————
         L.C.M               100   

   R. Mult. • R. Num.      251 • 10
   ——————————————————  =   ————————
         L.C.M               100   

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:

 (32•672) + 251 • 10     32•672 + 2510
 ———————————————————  =  —————————————
         100                  100     

Equation at the end of step  4  :

  (32•672 + 2510)    
  ——————————————— +  3
        100          

Step  5  :

Rewriting the whole as an Equivalent Fraction :

 5.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  100  as the denominator :

         3     3 • 100
    3 =  —  =  ———————
         1       100  

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

 5.2       Adding up the two equivalent fractions

 (201+2510) + 3 • 100     3011
 ————————————————————  =  ————
         100              100 

Final result :

  3011            
  ———— = 30.11000 
  100