Solution - Adding, subtracting and finding the least common multiple

Step  1  :

             7
 Simplify   ——
            20

Equation at the end of step  1  :

         16            7
  ((3 -  ——) -  4) -  ——
         25           20

Step  2  :

            16
 Simplify   ——
            25

Equation at the end of step  2  :

         16            7
  ((3 -  ——) -  4) -  ——
         25           20

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  25  as the denominator :

          3     3 • 25
     3 =  —  =  ——————
          1       25  

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:

 3 • 25 - (16)     59
 —————————————  =  ——
      25           25

Equation at the end of step  3  :

   59           7
  (—— -  4) -  ——
   25          20

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  25  as the denominator :

         4     4 • 25
    4 =  —  =  ——————
         1       25  

Adding fractions that have a common denominator :

 4.2       Adding up the two equivalent fractions

 59 - (4 • 25)     -41
 —————————————  =  ———
      25           25 

Equation at the end of step  4  :

  -41     7
  ——— -  ——
  25     20

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       25 

      The right denominator is :       20 

      Least Common Multiple:
      100 

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 = 4

   Right_M = L.C.M / R_Deno = 5

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.      -41 • 4
   ——————————————————  =   ———————
         L.C.M               100  

   R. Mult. • R. Num.      7 • 5
   ——————————————————  =   —————
         L.C.M              100 

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 -41 • 4 - (7 • 5)     -199
 —————————————————  =  ————
        100            100 

Final result :

  -199            
  ———— = -1.99000 
  100