Solution - Adding, subtracting and finding the least common multiple

Step  1  :

             5
 Simplify   ——
            16

Equation at the end of step  1  :

  4     2     5
  — ÷ (—— -  ——)
  5    25    16

Step  2  :

             2
 Simplify   ——
            25

Equation at the end of step  2  :

  4     2     5
  — ÷ (—— -  ——)
  5    25    16

Step  3  :

Calculating the Least Common Multiple :

 3.1    Find the Least Common Multiple

      The left denominator is :       25 

      The right denominator is :       16 

      Least Common Multiple:
      400 

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 = 16

   Right_M = L.C.M / R_Deno = 25

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.      2 • 16
   ——————————————————  =   ——————
         L.C.M              400  

   R. Mult. • R. Num.      5 • 25
   ——————————————————  =   ——————
         L.C.M              400  

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:

 2 • 16 - (5 • 25)     -93
 —————————————————  =  ———
        400            400

Equation at the end of step  3  :

  4   -93
  — ÷ ———
  5   400

Step  4  :

            4
 Simplify   —
            5

Equation at the end of step  4  :

  4   -93
  — ÷ ———
  5   400

Step  5  :

         4      -93
 Divide  —  by  ———
         5      400

 5.1    Dividing fractions

To divide fractions, write the divison as multiplication by the reciprocal of the divisor :

4     -93       4     400
—  ÷  ———   =   —  •  ———
5     400       5     -93

Final result :

  320            
  ——— = -3.44086 
  -93