Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "1.34" was replaced by "(134/100)". 3 more similar replacement(s)

Step  1  :

            67
 Simplify   ——
            50

Equation at the end of step  1  :

   216     464    67
  {———}2 + ———) + ——
   100     100    50

Step  2  :

            116
 Simplify   ———
            25 

Equation at the end of step  2  :

   216     116    67
  {———}2 + ———) + ——
   100     25     50

Step  3  :

            54
 Simplify   ——
            25

Equation at the end of step  3  :

    54       116     67
  ((——)2) +  ———) +  ——
    25       25      50

Step  4  :

 4.1     54 = 2•33

(54)² = (2•3³)² = 2² • 3⁶  4.2     25 = 5² (25)² = (5²)² = 5⁴

Equation at the end of step  4  :

   (22•36)    116     67
  (——————— +  ———) +  ——
     54       25      50

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       625 

      The right denominator is :       25 

      Least Common Multiple:
      625 

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 = 25

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.      2916
   ——————————————————  =   ————
         L.C.M             625 

   R. Mult. • R. Num.      116 • 25
   ——————————————————  =   ————————
         L.C.M               625   

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:

 2916 + 116 • 25     5816
 ———————————————  =  ————
       625           625 

Equation at the end of step  5  :

  5816    67
  ———— +  ——
  625     50

Step  6  :

Calculating the Least Common Multiple :

 6.1    Find the Least Common Multiple

      The left denominator is :       625 

      The right denominator is :       50 

      Least Common Multiple:
      1250 

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 = 2

   Right_M = L.C.M / R_Deno = 25

Making Equivalent Fractions :

 6.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      5816 • 2
   ——————————————————  =   ————————
         L.C.M               1250  

   R. Mult. • R. Num.      67 • 25
   ——————————————————  =   ———————
         L.C.M              1250  

Adding fractions that have a common denominator :

 6.4       Adding up the two equivalent fractions

 5816 • 2 + 67 • 25     13307
 ——————————————————  =  —————
        1250            1250 

Final result :

  13307            
  ————— = 10.64560 
  1250