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  :

          8     41
  (19 -  ——) -  ——
         10     10

Step  2  :

            4
 Simplify   —
            5

Equation at the end of step  2  :

         4     41
  (19 -  —) -  ——
         5     10

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  5  as the denominator :

           19     19 • 5
     19 =  ——  =  ——————
           1        5   

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 :

 3.2       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:

 19 • 5 - (4)     91
 ————————————  =  ——
      5           5 

Equation at the end of step  3  :

  91    41
  —— -  ——
  5     10

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       5 

      The right denominator is :       10 

      Least Common Multiple:
      10 

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.      91 • 2
   ——————————————————  =   ——————
         L.C.M               10  

   R. Mult. • R. Num.      41
   ——————————————————  =   ——
         L.C.M             10

Adding fractions that have a common denominator :

 4.4       Adding up the two equivalent fractions

 91 • 2 - (41)     141
 —————————————  =  ———
      10           10 

Final result :

  141            
  ——— = 14.10000 
  10