Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "9.8" was replaced by "(98/10)". 2 more similar replacement(s)

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                -(2/10)-((r-(98/10))/(-1))=0 

Step by step solution :

Step  1  :

            49
 Simplify   ——
            5 

Equation at the end of step  1  :

         2     49
  (0 -  ——) -  ——) ÷ -1  = 0 
        10     5 

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Subtracting a fraction from a whole

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

          r     r • 5
     r =  —  =  —————
          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 :

 2.2       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:

 r • 5 - (49)     5r - 49
 ————————————  =  ———————
      5              5   

Equation at the end of step  2  :

         2     (5r - 49)
  (0 -  ——) -  ————————— ÷ -1  = 0 
        10         5    

Step  3  :

         5r-49      
 Divide  —————  by  -1
           5        

Equation at the end of step  3  :

         2     (5r - 49)
  (0 -  ——) -  —————————  = 0 
        10        -5    

Step  4  :

            1
 Simplify   —
            5

Equation at the end of step  4  :

        1     (5r - 49)
  (0 -  —) -  —————————  = 0 
        5        -5    

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       5 

      The right denominator is :       -5 

      Least Common Multiple:
      5 

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 = -1

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.      -1
   ——————————————————  =   ——
         L.C.M             5 

   R. Mult. • R. Num.      (5r-49) • -1
   ——————————————————  =   ————————————
         L.C.M                  5      

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 -1 - ((5r-49) • -1)     5r - 50
 ———————————————————  =  ———————
          5                 5   

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   5r - 50  =   5 • (r - 10) 

Equation at the end of step  6  :

  r - 10  = 0 

Step  7  :

Solving a Single Variable Equation :

 7.1      Solve  :    r-10 = 0 

 Add  10  to both sides of the equation : 
                      r = 10

One solution was found :