Solution - Adding, subtracting and finding the least common multiple

Step  1  :

             9
 Simplify   ——
            10

Equation at the end of step  1  :

     2   4     9
  (0-—)-(—•(0-——))
     5   5    10

Step  2  :

            4
 Simplify   —
            5

Equation at the end of step  2  :

        2      4   -9
  (0 -  —) -  (— • ——)
        5      5   10

Step  3  :

            2
 Simplify   —
            5

Equation at the end of step  3  :

        2     -18
  (0 -  —) -  ———
        5     25 

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       5 

      The right denominator is :       25 

      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 = 5

   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.      -2 • 5
   ——————————————————  =   ——————
         L.C.M               25  

   R. Mult. • R. Num.      -18
   ——————————————————  =   ———
         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:

 -2 • 5 - (-18)      8
 ——————————————  =  ——
       25           25

Final result :

   8           
  —— = 0.32000 
  25