Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "4.1" was replaced by "(41/10)". 2 more similar replacement(s)

Step  1  :

            41
 Simplify   ——
            10

Equation at the end of step  1  :

   51      41
  {——}3 + (——)2)
   10      10

Step  2  :

 2.1     10 = 2•5 (10)² = (2•5)² = 2² • 5²

Equation at the end of step  2  :

   51       412  
  {——}3 + ———————
   10     (22•52)

Step  3  :

            51
 Simplify   ——
            10

Equation at the end of step  3  :

   51         412  
  (——)3) +  ———————
   10       (22•52)

Step  4  :

 4.1     51 = 3•17

(51)³ = (3•17)³ = 3³ • 17³  4.2     10 = 2•5 (10)³ = (2•5)³ = 2³ • 5³

Equation at the end of step  4  :

  (33•173)      412  
  ———————— +  ———————
  (23•53)     (22•52)

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       1000 

      The right denominator is :       100 

      Least Common Multiple:
      1000 

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 = 1

   Right_M = L.C.M / R_Deno = 10

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.      (33•173)
   ——————————————————  =   ————————
         L.C.M               1000  

   R. Mult. • R. Num.      1681 • 10
   ——————————————————  =   —————————
         L.C.M               1000   

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:

 (33•173) + 1681 • 10     33•173 + 16810
 ————————————————————  =  ——————————————
         1000                  1000     

Final result :

  51 + 16810
  ——————————
     1000