Solution - Adding, subtracting and finding the least common multiple

Step  1  :

             9
 Simplify   ——
            10

Equation at the end of step  1  :

  6     4     9
  — • (—— -  ——)
  7    10    10

Step  2  :

            2
 Simplify   —
            5

Equation at the end of step  2  :

  6    2     9
  — • (— -  ——)
  7    5    10

Step  3  :

Calculating the Least Common Multiple :

 3.1    Find the Least Common Multiple

      The left denominator is :       5 

      The right denominator is :       10 

      Least Common Multiple:
      10 

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 = 2

   Right_M = L.C.M / R_Deno = 1

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 • 2
   ——————————————————  =   —————
         L.C.M              10  

   R. Mult. • R. Num.       9
   ——————————————————  =   ——
         L.C.M             10

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 • 2 - (9)     -1
 ———————————  =  ——
     10          2 

Equation at the end of step  3  :

  6   -1
  — • ——
  7   2 

Step  4  :

            6
 Simplify   —
            7

Equation at the end of step  4  :

  6   -1
  — • ——
  7   2 

Step  5  :

Final result :

  -3            
  —— = -0.42857 
  7