Solution - Adding, subtracting and finding the least common multiple

Step  1  :

            1
 Simplify   —
            6

Equation at the end of step  1  :

   1 6     3 1
  (—-—) ÷ (—-—)
   2 5     2 6

Step  2  :

            3
 Simplify   —
            2

Equation at the end of step  2  :

   1    6     3    1
  (— -  —) ÷ (— -  —)
   2    5     2    6

Step  3  :

Calculating the Least Common Multiple :

 3.1    Find the Least Common Multiple

      The left denominator is :       2 

      The right denominator is :       6 

      Least Common Multiple:
      6 

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 = 3

   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.      3 • 3
   ——————————————————  =   —————
         L.C.M               6  

   R. Mult. • R. Num.      1
   ——————————————————  =   —
         L.C.M             6

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:

 3 • 3 - (1)     4
 ———————————  =  —
      6          3

Equation at the end of step  3  :

   1    6    4
  (— -  —) ÷ —
   2    5    3

Step  4  :

            6
 Simplify   —
            5

Equation at the end of step  4  :

   1    6    4
  (— -  —) ÷ —
   2    5    3

Step  5  :

            1
 Simplify   —
            2

Equation at the end of step  5  :

   1    6    4
  (— -  —) ÷ —
   2    5    3

Step  6  :

Calculating the Least Common Multiple :

 6.1    Find the Least Common Multiple

      The left denominator is :       2 

      The right denominator is :       5 

      Least Common Multiple:
      10 

Calculating Multipliers :

 6.2    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 = 2

Making Equivalent Fractions :

 6.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.       5
   ——————————————————  =   ——
         L.C.M             10

   R. Mult. • R. Num.      6 • 2
   ——————————————————  =   —————
         L.C.M              10  

Adding fractions that have a common denominator :

 6.4       Adding up the two equivalent fractions

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

Equation at the end of step  6  :

  -7   4
  —— ÷ —
  10   3

Step  7  :

         -7      4
 Divide  ——  by  —
         10      3

 7.1    Dividing fractions

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

-7     4       -7     3
——  ÷  —   =   ——  •  —
10     3       10     4

Final result :

  -21            
  ——— = -0.52500 
  40