Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "2.5" was replaced by "(25/10)". 2 more similar replacement(s)

Step by step solution :

Step  1  :

            5
 Simplify   —
            2

Equation at the end of step  1  :

     15             5
  (((——•r)-3r)+8r)+(—•r)  = 0 
     10             2

Step  2  :

            3
 Simplify   —
            2

Equation at the end of step  2  :

     3                       5r
  (((— • r) -  3r) +  8r) +  ——  = 0 
     2                       2 

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  2  as the denominator :

          3r     3r • 2
    3r =  ——  =  ——————
          1        2   

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:

 3r - (3r • 2)     -3r
 —————————————  =  ———
       2            2 

Equation at the end of step  3  :

   -3r           5r
  (——— +  8r) +  ——  = 0 
    2            2 

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  2  as the denominator :

          8r     8r • 2
    8r =  ——  =  ——————
          1        2   

Adding fractions that have a common denominator :

 4.2       Adding up the two equivalent fractions

 -3r + 8r • 2     13r
 ————————————  =  ———
      2            2 

Equation at the end of step  4  :

  13r    5r
  ——— +  ——  = 0 
   2     2 

Step  5  :

Adding fractions which have a common denominator :

 5.1       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:

 13r + 5r     18r
 ————————  =  ———
    2          2 

Reducing to Lowest Terms :

 5.2      The above result can still be reduced :

     18r      
     ——— = 9r 
      2       

Equation at the end of step  5  :

  9r  = 0 

Step  6  :

Solving a Single Variable Equation :

 6.1      Solve  :    9r = 0 

 Divide both sides of the equation by 9:
                     r = 0

One solution was found :