Dividing Monomials by Monomials and Polynomials

Dividing Monomials

Steps for Dividing Monomials

1. Divide the coefficients

2. Subtract the exponents of the common variables
   (Quotient rule for exponents)

In this case, there are no exponents to subtract because there are no variables on the bottom.

Subtract the exponents:

Divide the coefficients:

For r: 3 - 1 = 2
For s: 2 - 1 = 1
For t: 1 - 0 = 1

Subtract the exponents :

Divide the coefficients:

You Try!

Try these questions about dividing monomials!

Multiple Choice

Simplify: $$\frac{a^9}{a^5}$$  

• $$a^{14}$$  

• $$a^{45}$$  

• $$a^4$$  

• $$a^{\frac{9}{5}}$$  

Multiple Choice

Simplify: $$\frac{14x^5y}{2x^2y}$$  

• $$7x^3$$  

• $$7x^3y$$  

• $$12x^3$$  

• $$12x^3y$$  

Multiple Choice

Simplify: $$\frac{x^5y^4}{xy}$$  

• $$x^4y^3$$  

• $$x^5y^4$$  

Multiple Choice

• 4y⁶
• 4y²²
• 30y⁶
• 30y²²

Multiple Choice

Simplify.

• 6r⁶

• 3r⁴

• 3r⁶

• 6r⁴

Multiple Choice

Simplify: $$\frac{20x^5}{-10x^3}$$  

• $$-10x$$  

• $$2x^2$$  

• $$-2x^{2\ }$$  

• $$-2x^8$$  

Multiple Choice

Simplify: $$\frac{4a^4b^5c^8}{2a^2b^4c^6}$$  

• $$2a^8b^{20}c^{48}$$  

• $$2a^2bc^2$$  

Multiple Choice

Use the quotient rule to simplify the monomial.

• 5x²y

• -5x^2z

• -5x²yz

• 5xy²z

Multiple Choice

Use the quotient rule to simplify the monomial.

• -9b²

• 9b²

• -9a

• 9ab

Multiple Choice

Simplify: $$\frac{-16a^5b^9c^8}{2a^3b^3c^3}$$  

• $$-8a^8b^{12}c^{11}$$  

• $$8a^2b^6c^5$$  

• $$-14a^2b^6c^5$$  

• $$-8a^2b^6c^5$$  

Dividing Polynomials by Monomials

Dividing Polynomials by a monomial

When we divide a polynomials by a monomial, we divide each term in the numerator by the monomial in the denominator.

It's like dividing a bunch of monomials, like we just did!

You Try!

Try these questions about dividing polynomials by monomials!

Multiple Choice

$$\frac{50x\ -\ 30y\ +40z}{10}$$  

• $$5x\ -\ 3y\ +\ 4z$$  

• $$5\ -\ 3\ -\ 4$$  

• $$5x\ +\ 4y\ +\ 3z$$  

• $$40x\ -\ 20y\ -\ 30z$$  

Multiple Choice

$$\frac{-12a^{4\ }+\ 6a^3}{6a^3}$$  

• $$2a$$  

• $$-2a+1$$  

• $$2a\ +1$$  

• $$-2a\ +\ 1a$$  

Multiple Choice

$$\frac{-4a^{7\ }-\ 6a^5}{2a^3}$$  

• $$2a^{4\ }+3a^2$$  

• $$4a^{4\ }-\ 4a^2$$  

• $$-2a^{7\ }-\ 3a^5$$  

• $$-2a^{4\ }-3a^2$$  

Multiple Choice

$$\frac{18y^{6\ }+9y^{4\ }-12y^2}{3y^2}$$  

• $$6y^2\ +3y^2\ -4y^2$$  

• $$15y^{4\ }+6y^2\ -\ 9$$  

• $$6y^{4\ }+3y^2-4$$  

• $$6y^{3\ }-3y^2\ +4y$$  

Multiple Choice

$$\frac{4ab\ -\ 8b}{2b}$$  

• 2a + 4

• 2ab - 4

• 2a - 4

• 2a - 4b

Multiple Choice

$$\frac{6a^3b^2c^{4\ }-\ 8a^2b^2c}{2a^2bc}$$  

• $$3abc\ -\ 4abc$$  

• $$3abc^{3\ }-\ 4b$$  

• $$3a^3b^2c^{4\ }-\ 4b$$  

• $$3abc\ +4b$$  

Multiple Choice

$$\frac{20x^2yz\ +15xy^2z^2}{5xyz}$$  

• $$4x+3yz$$  

• $$4xyz\ +\ 3xyz$$  

• $$15x\ +12yz$$  

• $$4x^2yz\ +3xy^2z^2$$  

Poll

How are you feeling about dividing by monomials after today's lesson?

• I didn't get anything!

• I feel confused. I have questions

• I feel okay. I understand some things

• I get it. I am feeling good

• I get it completely. I feel like an expert!

Open Ended

Do you have any questions or comments about today's lesson?