1. Dividing Monomials
Chapter 5
Section 5.2

2. Objective
Students will simplify quotients of monomials and find the greatest common factor (GCF) of several monomials

3. Concept
There are three basic rules used to simplify fractions whose numerators and denominators are monomials. The property of quotients allows you to express a fraction as a product.

4. Concept
Property of Quotients If a, b, c, and d are real numbers with b ≠ 0 and d ≠ 0, then ac = a * c bd b d

5. Example
15 = 3 * 5 = 3 * 5 = 1 * 5 = *

6. Concept
You obtain the following rule for simplifying fractions if you let a=b in the property of quotients.

7. Concept
If b, c, and d are real numbers with b ≠ 0 and d ≠ 0, then bc = c bd d

8. Concept
This rule allows you to divide the numerator and denominator of a fraction by the same nonzero number. In the examples of this lesson, assume that no denominator equals zero.

9. Concept
A quotient of monomials is said to be simplified when each base appears only once, when there are no powers of powers, and when the numerator and denominator have no common factors other than 1.

10. Example
xy 10x

11. If m > n If n > m If m = n
Concept
Rule of Exponents for Division
If a is a nonzero real number and m and n are positive integers then:
If m > n If n > m If m = n
am = am-n am = am = 1
an an an-m an
always subtract the smaller exponent from the larger

12. Example
x9 x2 x3 x5 x7 x3

13. Example
35x3yz6 56x5yz

14. Example
(2ab)2 2ab2

15. Concept
The greatest common factor (GCF) of two or more monomials is the common factor with the greatest coefficient and the greatest degree in each variable. 1. Find the GCF of the numerical coefficients (prime factorization) 2. Find the smaller power of each variable in common 3. Write the product of the GCF and smaller power of variables

16. Find the GCF of 72x3yz3 and 120x2z5
Example
Find the GCF of 72x3yz3 and 120x2z5

17. Questions

18. Assignment
Worksheet