Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "5.8" was replaced by "(58/10)". 4 more similar replacement(s)

Step  1  :

            29
 Simplify   ——
            5 

Equation at the end of step  1  :

    89 118  34  29
  ((——+———)+——)+——
    10 10   10  5 

Step  2  :

            17
 Simplify   ——
            5 

Equation at the end of step  2  :

    89    118     17     29
  ((—— +  ———) +  ——) +  ——
    10    10      5      5 

Step  3  :

            59
 Simplify   ——
            5 

Equation at the end of step  3  :

    89    59     17     29
  ((—— +  ——) +  ——) +  ——
    10    5      5      5 

Step  4  :

            89
 Simplify   ——
            10

Equation at the end of step  4  :

    89    59     17     29
  ((—— +  ——) +  ——) +  ——
    10    5      5      5 

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       10 

      The right denominator is :       5 

      Least Common Multiple:
      10 

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.      89
   ——————————————————  =   ——
         L.C.M             10

   R. Mult. • R. Num.      59 • 2
   ——————————————————  =   ——————
         L.C.M               10  

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:

 89 + 59 • 2     207
 ———————————  =  ———
     10          10 

Equation at the end of step  5  :

   207    17     29
  (——— +  ——) +  ——
   10     5      5 

Step  6  :

Calculating the Least Common Multiple :

 6.1    Find the Least Common Multiple

      The left denominator is :       10 

      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 = 1

   Right_M = L.C.M / R_Deno = 2

Making Equivalent Fractions :

 6.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      207
   ——————————————————  =   ———
         L.C.M             10 

   R. Mult. • R. Num.      17 • 2
   ——————————————————  =   ——————
         L.C.M               10  

Adding fractions that have a common denominator :

 6.4       Adding up the two equivalent fractions

 207 + 17 • 2     241
 ————————————  =  ———
      10          10 

Equation at the end of step  6  :

  241    29
  ——— +  ——
  10     5 

Step  7  :

Calculating the Least Common Multiple :

 7.1    Find the Least Common Multiple

      The left denominator is :       10 

      The right denominator is :       5 

      Least Common Multiple:
      10 

Calculating Multipliers :

 7.2    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 :

 7.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      241
   ——————————————————  =   ———
         L.C.M             10 

   R. Mult. • R. Num.      29 • 2
   ——————————————————  =   ——————
         L.C.M               10  

Adding fractions that have a common denominator :

 7.4       Adding up the two equivalent fractions

 241 + 29 • 2     299
 ————————————  =  ———
      10          10 

Final result :

  299            
  ——— = 29.90000 
  10