Solution - Adding, subtracting and finding the least common multiple

Step  1  :

             7
 Simplify   ——
            10

Equation at the end of step  1  :

  1     15     7
  — +  (—— -  ——)
  6     15    10

Step  2  :

            1
 Simplify   —
            1

Equation at the end of step  2  :

  1           7
  — +  (1 -  ——)
  6          10

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  10  as the denominator :

          1     1 • 10
     1 =  —  =  ——————
          1       10  

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 :

 3.2       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:

 10 - (7)      3
 ————————  =  ——
    10        10

Equation at the end of step  3  :

  1     3
  — +  ——
  6    10

Step  4  :

            1
 Simplify   —
            6

Equation at the end of step  4  :

  1     3
  — +  ——
  6    10

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       6 

      The right denominator is :       10 

      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 = 5

   Right_M = L.C.M / R_Deno = 3

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.       5
   ——————————————————  =   ——
         L.C.M             30

   R. Mult. • R. Num.      3 • 3
   ——————————————————  =   —————
         L.C.M              30  

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 5 + 3 • 3      7
 —————————  =  ——
    30         15

Final result :

   7           
  —— = 0.46667 
  15