Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "0.47" was replaced by "(47/100)". 4 more similar replacement(s)

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

           (43/100)+(27/10)*w-((37/10)*w-(47/100))=0 

Step by step solution :

Step  1  :

             47
 Simplify   ———
            100

Equation at the end of step  1  :

    43  27       37     47
  (———+(——•w))-((——•w)-———)  = 0 
   100  10       10    100

Step  2  :

            37
 Simplify   ——
            10

Equation at the end of step  2  :

    43  27       37     47
  (———+(——•w))-((——•w)-———)  = 0 
   100  10       10    100

Step  3  :

Calculating the Least Common Multiple :

 3.1    Find the Least Common Multiple

      The left denominator is :       10 

      The right denominator is :       100 

      Least Common Multiple:
      100 

Calculating Multipliers :

 3.2    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 = 10

   Right_M = L.C.M / R_Deno = 1

Making Equivalent Fractions :

 3.3      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.      37w • 10
   ——————————————————  =   ————————
         L.C.M               100   

   R. Mult. • R. Num.       47
   ——————————————————  =   ———
         L.C.M             100

Adding fractions that have a common denominator :

 3.4       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:

 37w • 10 - (47)     370w - 47
 ———————————————  =  —————————
       100              100   

Equation at the end of step  3  :

    43     27          (370w - 47)
  (——— +  (—— • w)) -  ———————————  = 0 
   100     10              100    

Step  4  :

            27
 Simplify   ——
            10

Equation at the end of step  4  :

    43     27          (370w - 47)
  (——— +  (—— • w)) -  ———————————  = 0 
   100     10              100    

Step  5  :

             43
 Simplify   ———
            100

Equation at the end of step  5  :

    43    27w     (370w - 47)
  (——— +  ———) -  ———————————  = 0 
   100    10          100    

Step  6  :

Calculating the Least Common Multiple :

 6.1    Find the Least Common Multiple

      The left denominator is :       100 

      The right denominator is :       10 

      Least Common Multiple:
      100 

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 = 10

Making Equivalent Fractions :

 6.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.       43
   ——————————————————  =   ———
         L.C.M             100

   R. Mult. • R. Num.      27w • 10
   ——————————————————  =   ————————
         L.C.M               100   

Adding fractions that have a common denominator :

 6.4       Adding up the two equivalent fractions

 43 + 27w • 10     270w + 43
 —————————————  =  —————————
      100             100   

Equation at the end of step  6  :

  (270w + 43)    (370w - 47)
  ——————————— -  ———————————  = 0 
      100            100    

Step  7  :

Adding fractions which have a common denominator :

 7.1       Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

 (270w+43) - ((370w-47))     90 - 100w
 ———————————————————————  =  —————————
           100                  100   

Step  8  :

Pulling out like terms :

 8.1     Pull out like factors :

   90 - 100w  =   -10 • (10w - 9) 

Equation at the end of step  8  :

  -10 • (10w - 9)
  ———————————————  = 0 
        100      

Step  9  :

When a fraction equals zero :

 9.1    When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

  -10•(10w-9)
  ——————————— • 100 = 0 • 100
      100    

Now, on the left hand side, the  100  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
   -10  •  (10w-9)  = 0

Equations which are never true :

 9.2      Solve :    -10   =  0

This equation has no solution.
A a non-zero constant never equals zero.

Solving a Single Variable Equation :

 9.3      Solve  :    10w-9 = 0 

 Add  9  to both sides of the equation : 
                      10w = 9
Divide both sides of the equation by 10:
                     w = 9/10 = 0.900

One solution was found :