Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "0.8" was replaced by "(8/10)". 2 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 :

           (21/7)/((15/10)*a)-(5/14/(8/10))=0 

Step by step solution :

Step  1  :

            4
 Simplify   —
            5

Equation at the end of step  1  :

  21    15     5   4
  —— ÷ (——•a)-—— ÷ —  = 0 
  7     10    14   5

Step  2  :

             5
 Simplify   ——
            14

Equation at the end of step  2  :

  21    15     5   4
  —— ÷ (——•a)-—— ÷ —  = 0 
  7     10    14   5

Step  3  :

          5      4
 Divide  ——  by  —
         14      5

 3.1    Dividing fractions

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

 5     4        5     5
——  ÷  —   =   ——  •  —
14     5       14     4

Equation at the end of step  3  :

  21    15        25
  —— ÷ (—— • a) - ——  = 0 
  7     10        56

Step  4  :

            3
 Simplify   —
            2

Equation at the end of step  4  :

  21    3        25
  —— ÷ (— • a) - ——  = 0 
  7     2        56

Step  5  :

            3
 Simplify   —
            1

Equation at the end of step  5  :

  3a    25
  —— -  ——  = 0 
  2     56

Step  6  :

                3a
 Divide  3  by  ——
                2 

Equation at the end of step  6  :

  2    25
  — -  ——  = 0 
  a    56

Step  7  :

Calculating the Least Common Multiple :

 7.1    Find the Least Common Multiple

      The left denominator is :       a 

      The right denominator is :       56 

      Least Common Multiple:
      56a 

Calculating Multipliers :

 7.2    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 = 56

   Right_M = L.C.M / R_Deno = a

Making Equivalent Fractions :

 7.3      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.      2 • 56
   ——————————————————  =   ——————
         L.C.M              56a  

   R. Mult. • R. Num.      25 • a
   ——————————————————  =   ——————
         L.C.M              56a  

Adding fractions that have a common denominator :

 7.4       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:

 2 • 56 - (25 • a)     112 - 25a
 —————————————————  =  —————————
        56a               56a   

Equation at the end of step  7  :

  112 - 25a
  —————————  = 0 
     56a   

Step  8  :

When a fraction equals zero :

 8.1    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:

  112-25a
  ——————— • 56a = 0 • 56a
    56a  

Now, on the left hand side, the  56a  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
   112-25a  = 0

Solving a Single Variable Equation :

 8.2      Solve  :    -25a+112 = 0 

 Subtract  112  from both sides of the equation : 
                      -25a = -112
Multiply both sides of the equation by (-1) :  25a = 112


Divide both sides of the equation by 25:
                     a = 112/25 = 4.480

One solution was found :