Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "5.4" was replaced by "(54/10)". 3 more similar replacement(s)

Step  1  :

            27
 Simplify   ——
            5 

Equation at the end of step  1  :

   42    89     27
  (—— +  ——) +  ——
   10    10     5 

Step  2  :

            89
 Simplify   ——
            10

Equation at the end of step  2  :

   42    89     27
  (—— +  ——) +  ——
   10    10     5 

Step  3  :

            21
 Simplify   ——
            5 

Equation at the end of step  3  :

   21    89     27
  (—— +  ——) +  ——
   5     10     5 

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       5 

      The right denominator is :       10 

      Least Common Multiple:
      10 

Calculating Multipliers :

 4.2    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 = 2

   Right_M = L.C.M / R_Deno = 1

Making Equivalent Fractions :

 4.3      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.      21 • 2
   ——————————————————  =   ——————
         L.C.M               10  

   R. Mult. • R. Num.      89
   ——————————————————  =   ——
         L.C.M             10

Adding fractions that have a common denominator :

 4.4       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:

 21 • 2 + 89     131
 ———————————  =  ———
     10          10 

Equation at the end of step  4  :

  131    27
  ——— +  ——
  10     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

   L. Mult. • L. Num.      131
   ——————————————————  =   ———
         L.C.M             10 

   R. Mult. • R. Num.      27 • 2
   ——————————————————  =   ——————
         L.C.M               10  

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 131 + 27 • 2     37
 ————————————  =  ——
      10          2 

Final result :

  37            
  —— = 18.50000 
  2