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Solution - Adding, subtracting and finding the least common multiple

\frac{59}{1000} = 0.05900

59/1000=0.05900

Step by Step Solution

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-2" was replaced by "^(-2)".

(2): "0.029" was replaced by "(029/1000)".

Step 1 :

 1.1     10 = 2•5

(10)^-2 = (2•5)^(-2) = (2)^(-2) • (5)^(-2)

Equation at the end of step 1 :

   29     
  ———— +  (3 • ((2)^(-2)•(5)^(-2)))
  1000

Step 2 :

Equation at the end of step 2 :

   29      3 
  ———— +  ———
  1000    100

Step 3 :

             29 
 Simplify   ————
            1000

Equation at the end of step 3 :

   29      3 
  ———— +  ———
  1000    100

Step 4 :

Calculating the Least Common Multiple :

4.1    Find the Least Common Multiple

      The left denominator is :       1000

      The right denominator is :       100

Number of times each prime factor
appears in the factorization of:
Prime Factor	Left Denominator	Right Denominator	L.C.M = Max {Left,Right}
2	3	2	3
5	3	2	3
Product of all Prime Factors	1000	100	1000

Least Common Multiple:
1000

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 = 1

   Right_M = L.C.M / R_Deno = 10

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.       29 
   ——————————————————  =   ————
         L.C.M             1000

   R. Mult. • R. Num.      3 • 10
   ——————————————————  =   ——————
         L.C.M              1000

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:

 29 + 3 • 10      59 
 ———————————  =  ————
    1000         1000

Final result :

   59            
  ———— = 0.05900 
  1000

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