Dividing Monomials

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Dividing monomials deals with the problems of dividing monomial expressions. Monomial expression is an expression consists of single term. Dividing monomials is the basic concept on dividing polynomials. Use laws of exponent on dividing variables.  Monomial division starts with dividing the coefficients and for dividing variables we must follow the rules of exponents which means when we divide like variable subtract the powers.
The following examples clearly illustrate the steps involved in dividing monomials.

Example 1: Divide (12x^3y^-2) / 4y^-1x^2

Solution: First divide the coefficients 12/-4 = 3

Then divide the variables (like terms)

As per law of exponents, subtract the powers on division.

x^3 / x^2 = x^1 = x

y^-2 / y^-1 = y^-2-(-1) = y^-1

Therefore the answer is 3xy^-1
 
Example 2: The area of a rectangle is 48s^7t^4. If length of rectangle is 8s^4t then what is the width of the rectangle?

Solution: The area of rectangle = 48s^7t^4

The length of rectangle = 8s^4t

We know Area = length * width

Here length and Area is given.

Plug in the values, we get, 48s^7t^4 = 8s^4t / w

Width w = 48s^7t^4 / 8s^4t

First divide the coefficients and then divide the variables, 48/8 = 5

 s^7t^4 /  s^4t = s^3 t^3

Therefore the width of rectangle is 5s^3 t^3

Example 3: Divide 24x^3y^5z / -2xy^3

Solution: Divide the coefficient = 24/2 = -12

Now divide the variables x^3y^5z / xy^3 = x^2y^2z      
  
The answer is -12 x^2y^2z

Note: Take care of signs while dividing the coefficients.

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