Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "4.7" was replaced by "(47/10)". 2 more similar replacement(s)

Step  1  :

            47
 Simplify   ——
            10

Equation at the end of step  1  :

         3005     47     
  ((0 -  ————) -  ——) +  -2
         1000     10     

Step  2  :

            601
 Simplify   ———
            200

Equation at the end of step  2  :

         601     47     
  ((0 -  ———) -  ——) +  -2
         200     10     

Step  3  :

Calculating the Least Common Multiple :

 3.1    Find the Least Common Multiple

      The left denominator is :       200 

      The right denominator is :       10 

      Least Common Multiple:
      200 

Calculating Multipliers :

 3.2    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 = 20

Making Equivalent Fractions :

 3.3      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.      -601
   ——————————————————  =   ————
         L.C.M             200 

   R. Mult. • R. Num.      47 • 20
   ——————————————————  =   ———————
         L.C.M               200  

Adding fractions that have a common denominator :

 3.4       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:

 -601 - (47 • 20)     -1541
 ————————————————  =  —————
       200             200 

Equation at the end of step  3  :

  -1541    
  ————— +  -2
   200     

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  200  as the denominator :

          -2     -2 • 200
    -2 =  ——  =  ————————
          1        200   

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 :

 4.2       Adding up the two equivalent fractions

 -1541 + -2 • 200     -1941
 ————————————————  =  —————
       200             200 

Final result :

  -1941            
  ————— = -9.70500 
   200