Solution - Adding, subtracting and finding the least common multiple

Step  1  :

            2
 Simplify   —
            5

Equation at the end of step  1  :

    11  8  7  2
  ((——-——)+—)-—
    30 15  6  5

Step  2  :

            7
 Simplify   —
            6

Equation at the end of step  2  :

    11     8     7     2
  ((—— -  ——) +  —) -  —
    30    15     6     5

Step  3  :

             8
 Simplify   ——
            15

Equation at the end of step  3  :

    11     8     7     2
  ((—— -  ——) +  —) -  —
    30    15     6     5

Step  4  :

            11
 Simplify   ——
            30

Equation at the end of step  4  :

    11     8     7     2
  ((—— -  ——) +  —) -  —
    30    15     6     5

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       30 

      The right denominator is :       15 

      Least Common Multiple:
      30 

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 = 1

   Right_M = L.C.M / R_Deno = 2

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.      11
   ——————————————————  =   ——
         L.C.M             30

   R. Mult. • R. Num.      8 • 2
   ——————————————————  =   —————
         L.C.M              30  

Adding fractions that have a common denominator :

 5.4       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:

 11 - (8 • 2)     -1
 ————————————  =  ——
      30          6 

Equation at the end of step  5  :

   -1    7     2
  (—— +  —) -  —
   6     6     5

Step  6  :

Adding fractions which have a common denominator :

 6.1       Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

 -1 + 7     1
 ——————  =  —
   6        1

Equation at the end of step  6  :

  1    2
  — -  —
  1    5

Step  7  :

Rewriting the whole as an Equivalent Fraction :

 7.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  5  as the denominator :

          1     1 • 5
     1 =  —  =  —————
          1       5  

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 :

 7.2       Adding up the two equivalent fractions

 5 - (2)     3
 ———————  =  —
    5        5

Final result :

  3           
  — = 0.60000 
  5