Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "1.62" was replaced by "(162/100)". 3 more similar replacement(s)

Step  1  :

            81
 Simplify   ——
            50

Equation at the end of step  1  :

  414   575    81
  ——— ÷ ——— + (——)2)
  100   100    50

Step  2  :

 2.1     81 = 34

(81)² = (3⁴)² = 3⁸  2.2     50 = 2•5² (50)² = (2•5²)² = 2² • 5⁴

Equation at the end of step  2  :

  414   575      38  
  ——— ÷ ——— + ———————
  100   100   (22•54)

Step  3  :

            23
 Simplify   ——
            4 

Equation at the end of step  3  :

  414   23      38  
  ——— ÷ —— + ———————
  100   4    (22•54)

Step  4  :

            207
 Simplify   ———
            50 

Equation at the end of step  4  :

  207   23       38  
  ——— ÷ —— +  ———————
  50    4     (22•54)

Step  5  :

         207      23
 Divide  ———  by  ——
         50       4 

 5.1    Dividing fractions

To divide fractions, write the divison as multiplication by the reciprocal of the divisor :

207     23       207      4
———  ÷  ——   =   ———  •  ——
50      4        50      23

Equation at the end of step  5  :

  18       38  
  —— +  ———————
  25    (22•54)

Step  6  :

Calculating the Least Common Multiple :

 6.1    Find the Least Common Multiple

      The left denominator is :       25 

      The right denominator is :       2500 

      Least Common Multiple:
      2500 

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 = 100

   Right_M = L.C.M / R_Deno = 1

Making Equivalent Fractions :

 6.3      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.      18 • 100
   ——————————————————  =   ————————
         L.C.M               2500  

   R. Mult. • R. Num.      6561
   ——————————————————  =   ————
         L.C.M             2500

Adding fractions that have a common denominator :

 6.4       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:

 18 • 100 + 6561     8361
 ———————————————  =  ————
      2500           2500

Final result :

  8361           
  ———— = 3.34440 
  2500