Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "9.7" was replaced by "(97/10)". 3 more similar replacement(s)

Step  1  :

            97
 Simplify   ——
            10

Equation at the end of step  1  :

      328     44      97
  ((0-———)-(0-——))+(0-——)
      100     10      10

Step  2  :

            22
 Simplify   ——
            5 

Equation at the end of step  2  :

         328           22      -97
  ((0 -  ———) -  (0 -  ——)) +  ———
         100           5       10 

Step  3  :

            82
 Simplify   ——
            25

Equation at the end of step  3  :

         82     -22     -97
  ((0 -  ——) -  ———) +  ———
         25      5      10 

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       25 

      The right denominator is :       5 

      Least Common Multiple:
      25 

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 = 5

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.      -82
   ——————————————————  =   ———
         L.C.M             25 

   R. Mult. • R. Num.      -22 • 5
   ——————————————————  =   ———————
         L.C.M               25   

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:

 -82 - (-22 • 5)     28
 ———————————————  =  ——
       25            25

Equation at the end of step  4  :

  28    -97
  —— +  ———
  25    10 

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       25 

      The right denominator is :       10 

      Least Common Multiple:
      50 

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 = 2

   Right_M = L.C.M / R_Deno = 5

Making Equivalent Fractions :

 5.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      28 • 2
   ——————————————————  =   ——————
         L.C.M               50  

   R. Mult. • R. Num.      -97 • 5
   ——————————————————  =   ———————
         L.C.M               50   

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 28 • 2 + -97 • 5     -429
 ————————————————  =  ————
        50             50 

Final result :

  -429            
  ———— = -8.58000 
   50