The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

Teaching Notes 5.10: Dividing Monomials

The process of dividing monomials involves subtracting the exponents of common bases.

Confusion arises when students wonder why they are subtracting when they are supposed to be

dividing.

1. Review the property of exponents for multiplication,xm·xn=xm+n. Present examples such
   as 3x^2 · 4 x^8. Note that the product 12x^10 was found by multiplying the coefficients of the
   terms and adding the exponents of the common bases. Provide more examples if necessary.


2. Explain that division is the inverse, or opposite, operation of multiplication. When dividing
   monomials, instead of multiplying the coefficients as in multiplication, students divide or
   simplify the coefficients. Instead of adding the exponents as in multiplication, they sub-

tract the exponents when dividing. Introduce the property of exponents for division,

xm

xn

=

xm−nwherex=0.

3. Explain that all powers of powers must be simplified before monomials can be divided.

Provide examples such as

(2x^2 )^3

3 x

, which must be simplified to

8 x^6

3 x

before dividing. You might

also find it helpful to review 5.6: ‘‘Using Powers of Monomials.’’

4. Review the information and example on the worksheet with your students.

EXTRA HELP:

Check your work by multiplying the quotient by the divisor. The answer should equal the monomial

in the numerator.

ANSWER KEY:

(1) 2 x (2) 7 x (3) 250 a^5 (4) 1 (5)z^2 (6) 3 a^7

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(Challenge)Rebecca’s answer is incorrect. She should have subtracted the exponents rather

than divided them.

18 x^4 y^10

9 x^4 y^5

= 2 y^5

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194 THE ALGEBRA TEACHER’S GUIDE